WO2010134828A1 - Three-dimensional logical puzzle and the method of determining shape of its pieces - Google Patents

Abstract

The invention relates to a three-dimensional puzzle whose outer layer is divided into a series of elements some of which are movable. The movable elements of at least two different shapes are arranged in n = 6 or 4 mutually intersecting circular rings encircling the puzzle. The rings run according to great circles determined on a sphere by its intersections with planes that are parallel to faces of a regular dodecahedron or octahedron circumscribed around the sphere. In the spaces between the rings there are additional single filling elements of at most two different types (3 _n ) and (7 _n ). They are immovable and constitute the outermost elements of the central base body. The movable ring pieces (4 _n ) and (5 _n ) are interlocked with them and with each other with the help of extensions (8 _n ), (9 _n ) placed on their back invisible sides. A principle of the puzzle operation consists in sliding relocation of the movable elements through sequential rotations of the rings around the puzzle centre through an angle of 360/(n-1) degrees. In particular, the invention concerns the puzzle resembling a standard football, that is a solid consisting of 12 pentagons and 20 hexagons as well as some other polyhedral solids and their spherical equivalents. In a version representing the typical football the hexagons are created from the movable triangle elements (4₆) and from halves of the movable rhomboidal elements (5₆). The ring movement consists in simultaneous relocation of the rhomboidal (5₆) and triangular (4₆) elements alternating in the ring. The invention also relates to a method of determining the geometrical shape of the puzzle pieces.

Description

Three-dimensional logical puzzle and the method of determining shape of its pieces

The present invention is a three-dimensional puzzle consisting of a number of shape fitting pieces that can change their position on the puzzle surface by rotatable movements of their groups around axes crossing the centre of the puzzle. The invention also concerns the method of determining geometrical shape of the puzzle's pieces.

The most widely known three-dimensional puzzle with movable elements is the coloured cuboid 3x3x3 puzzle, called 'Rubik's cube', as well as its numerous variants based on regular polyhedrons, also spherically shaped. These puzzles use single rotating movements of groups of elements forming layers that are parallel to polyhedron faces. Puzzle construction is based on a central body whose outermost elements are the central pieces of rotating layers. Movable elements are interlocked with the central body and with the adjacent pieces by means of projections (extensions) placed on their bottom (back) sides.

Among published puzzle solutions of a spherical shape there are puzzles with three rings on their surface which are perpendicular to each other, each consisting of a plurality of elements, most frequently in the shape of a square. The pieces can move on a spherical surface by rotation around the puzzle centre of all elements belonging to a given ring. US5074562 or US5452895 present examples of such solutions. The puzzles in publications US5836584 or US5566941 are additionally divided into two semi-spherical parts that can rotate relative to each other and the puzzle in publication FR2724573 in addition has six rotating caps.

Another type of a spherical puzzle is one whose outer layer is divided into a plurality of elements by 3 or 5 latitudinal lines and 3 to 4 longitudinal lines treated as full circles. Examples of such a solution are presented in publications EP0069727 or US4865323, where elements can move by rotation around a polar axis within the layer set by two neighbouring latitudinal circles and can change the layer they belong to into a symmetric one located on the opposite side relative to the equator, by a half turn of one semi-spherical part relative to another one along the longitudinal circle. The technical solutions presented in both mentioned publications consist in joining appropriately shaped elements to each other and/or to the central body by means of dovetail projections that enable sliding movements of the projections along a circle channel created by grooves of the adjacent elements.

A family of a different type of spherical puzzles having rotatable, partially overlapping caps, each consisting of several elements that are cut out of a sphere by planes parallel to faces of regular polyhedrons circumscribed on the sphere, is presented in publication DE3127757 of year 1983. The pieces are joined to each other by dovetail projections which enable their sliding movement along circle trajectories created by grooves of the adjacent elements. Or, alternatively, by means of a central body in the shape of another ball placed inside the puzzle. The ball has holes in the places corresponding to the centres of the rotating elements. Playing with the puzzle consists in sequential rotations of the caps around their axes of symmetry. A particular case of the puzzle belonging to the family was patented in January 2002, publication number EP0874672. The puzzle is created from a hollow ball, where 8 caps are separated by planes of faces of a regular octahedron inscribed within the outer sphere. Each cap consists of 4 movable elements: three permuting pieces of the shape similar to a cross- section of a convex lens and the fourth rotating piece placed between them, whose shape is that of a spherical triangle with arched concave sides. The pieces are joined to each other by dovetail grooves and projections. Another solution published in 2004 with number WO2004110575 is the family of puzzles where a hollow ball or polyhedron was divided according to different schemes into caps and equatorial rings or groups of rings consisting of an equatorial ring and latitudinal rings between caps. The technical solution consists in joining of the elements one to another by dovetail projections and grooves that enable sliding movements of projections along circular trajectories created by grooves of adjacent elements. A similar solution, presented in publication WO2008026218 of February 2008, is a puzzle in the shape of a hollow ball that is divided into a plurality of movable elements by 8 circles with their centres located pairwise on 4 axes crossing the centre of the puzzle and perpendicular to the faces of the regular octahedron circumscribed on the ball, where each pair of the centres of these circles divides the sphere's diameter into three equal parts. The puzzle elements are dovetailed to each other. The three-dimensional puzzle of the present invention consists of the shape fitting elements, some of which are movable, and where the movable elements of at least two different shapes are arranged in π = 6 or 4 mutually intersecting circular rings encircling the puzzle body. The movable elements relocate by sliding movements consisting in 360/(n-1 ) degree sequential ring turns around the puzzle centre. The puzzle rings run according to the great circles presented in fιg.1 or fig. 2, which circles constitute the circular trajectories for the rings' movements. The circles in turn are determined by the lines of the intersection of the sphere with the planes running through the centre of the sphere (and the centre of the puzzle at the same time) parallel to the faces of a regular dodecahedron (fig.1) or regular octahedron (fig.2) circumscribed on the sphere in both cases. All trajectories of the chosen puzzle, and then its rings, intersect mutually at the same angle, different from the right angle, and each circular trajectory intersects each of the other ones at two points lying on the opposite sphere sides, where each intersection marked on fig.1 and fιg.2 with the symbol C_n belongs to at most two trajectories. The lower index n refers to the number of rings in the puzzle. So, there are 2(n-1) intersections on each trajectory which are distributed in equal intervals. The rings are of the same width and in the case of the puzzle Ue they are symmetric relative to their trajectories, that is, the trajectory plane fe (fig.3) constitutes the plane of ring symmetry. As for the puzzle IU, the ring symmetry condition does not need to be satisfied. The mentioned trajectories determine two kinds of figures on the sphere: the smaller triangular figures whose centres are denoted with symbols A_n and the bigger ones which for n = 6 are pentagonal, whereas for n = 4 they are quadrangular, and whose centres are marked with symbols B_n (fig.1 , fig.2). Symbols α_n and β_n (fιg.3, fig.4) denote the smallest positive acute angles that are created by the trajectory plane t_n and the sphere axes a_n and b_n that pass through points A_n and B_n respectively. The width of the rings can be arbitrary, however the present invention is limited to the puzzle whose movable ring elements do not exceed the arms of angle 2β_n, which is symmetric relative to the ring trajectory plane t_n and has its vertex in the centre of the puzzle.

The fact that the ring width corresponds to an angle lower than 2β_n causes empty spaces between the rings around axes b_n. The spaces are filled with additional single elements. In fig.5 - fig.12 they are the bigger elements marked with dark colour or just the only elements marked that way. They occupy the places denoted with symbols B_n and will be referred to as basic elements hereafter. They are of a pentagonal shape if they belong to the puzzle Uε, and then there are 3*(6-2) = 12 of them or of a quadrangular shape if they belong to the puzzle U₄, and then there are 3^*(4-2) = 6 of such pieces: in general 3(n-2) elements. In the figures, they are denoted with symbols 3β and 3₄ respectively. In the present invention, the basic elements 3_n are immovable and unpivotable and constitute the outermost parts of its central body, which will be elaborated in further part of the description.

The main logical elements of the puzzle according to the present invention, while resting, are situated on the trajectory intersections marked with symbols C_n. They are denoted with the symbol 5_n (fig.5 - fig.12) and referred to hereafter as movable elements of sort I. In the resting position they belong simultaneously to two rings and can relocate into any intersection C_n of the trajectories. The puzzle Ue has 6^*5 = 30 such elements, whereas the puzzle U₄ has 4*3 =12 of them, in general n(n-1) pieces. Each ring contains as many of them as many intersections with other rings it has, which yields the number of 2(n-1), that is, 10 or 6 respectively. Between any two neighbouring elements 5_n there are other movable elements in the ring, whose number, sort and shape depend on the width and symmetry of the rings of a given puzzle. Because of that, each ring contains at least twice as many elements as there are intersections with other rings, which yields 4(n-1) of the pieces, that is, at least 20 in the puzzle Ue and at least 12 in the puzzle U₄. Visible elements which, when resting, fit tight to the sides of the basic elements, are movable elements of sort II. They are marked with the symbol A_n and constitute the second type of ring elements (fig.5 - fig.12). There are as many of them in the ring as there are movable elements of sort I₁ because the two types alternate. However there are twice as many of them in the puzzle as there are elements 5_n, because in the resting position each element A_n belongs only to one ring, which yields the number of 2n(n-1) pieces, that is, 60 or 24 respectively.

The internal construction of the puzzle according to the invention, in the majority, uses spherical and conical shapes. To a small degree it depends on the external shape of the puzzle surface, of which it is only required that it should fall in-between two concentric spheres with their centre situated in the centre of the puzzle. To focus the attention, the description of the invention concentrates on the spherically shaped puzzle for which both spheres coincide. Therefore whenever it is referred herein to polygonal figures or polyhedral solids, in the majority they are parts of spherical or conical surfaces, they result from the intersections of such surfaces and/or they are limited by such surfaces. Puzzle variants in polyhedral shapes are presented at the end of the description.

The particular case of the puzzle is obtained when the ring width on its surface corresponds to the angle of 2α_n, that is, when visible borders of the resting rings intersect the axes a_n. For n = 6 such a puzzle Uβ_/i is presented in fig.5, and for n = 4 a puzzle U4/1 is shown in fig.8. Visible parts of I sort elements 5_n take on a rhomboidal shape then and Il sort elements A_n become triangles that for n = 6 are close to an equilateral one. When two identical complementary acute-angled triangles are distinguished on the surface of each element 5_n with the help of the shorter diagonal, then 2π(π-1)/3 (that is 20 or 8) hexagons appear on the puzzle surface. Such , a variant of the puzzle U_4/1 is presented in fig.13. For n = 6 it gives a pattern corresponding to a standard football, that is, a ball whose surface consists of 12 pentagons and 20 hexagons surrounding the pentagons, which is depicted in fig.14. Fig.39c shows a polyhedral equivalent of such a variant of the puzzle Uβ_/i- Each hexagon is created by three triangular pieces 4_n and three halves of the pieces 5_n. These elements belong to three rings meeting in the hexagon. In the case of the puzzle Uεn the elements 5β as well as halves of the elements 4β take . on the shape close to the equilateral triangle and thus they form almost regular hexagons between pentagons. The analogous variant of the puzzle U4_/1 does not have such a property, where the angle of 2α₄ corresponds to Il sort elements of the shape of an elongated isosceles triangle (fig.8, fig.13). Each hexagon shares three rhomboidal elements with three other hexagons that are adjacent to it. If each hexagon consisting of six triangles is covered with a colour different from the colours of the adjacent hexagons then all rhomboidal elements are two-coloured, similarly to edge blocks in Rubik's cube (the rhomboidal elements of a polyhedral variant presented in fig.39c are edge elements). To achieve such an effect four colours are sufficient. The remaining triangle elements are uni-coloured in such a case. To achieve equal and evenly spread number of the elements of each colour, 5, 10 or 20 different colours should be used in the case of the puzzle Uβ/i and 4 or 8 ones in the case of U_4/1. Using only 5 or 4 colours respectively makes the puzzles simpler as then there are groups of the identical two-coloured rhomboidal elements of n/2 number each, that is, groups of elements having the same pair of colours on their surface. Using 10 colours in the case of Uβ/i and 8 colours in the case of U4/1 allows for the unique set of colours of all rhomboidal elements. Instead of colours any set of patterns or textures can be used.

When the puzzle rings are narrow enough to have their elements included inside the arms of angle 2α_n symmetric relative to the plane t_n and with its vertex at the centre of the sphere, then the axes a_n are situated outside the rings and empty spaces appear between the rings around the mentioned axes. The spaces are filled with another type of single elements 7_n of the shape of a triangle with convex sides. In the puzzles Uβ/∑- and U4/2 presented in fig.6 and fig.9, these elements belong to the outer puzzle layer, whereas in some other puzzle variants they are invisible (fig.20, fig.22). The latter occurs when ring elements do not touch arms of the angle 2α_n only in deeper puzzle layers. Similarly to the basic elements, the elements 7_n are immovable. They will be referred to as supplementary elements hereafter. In the considered' case of the ring width, the number of the visible supplementary elements I_n is equal to the number of the points A_n on the sphere, that is, 20 or 8 respectively.

If the ring elements exceed the arms of the angle 2α_n, then each axis a_n simultaneously penetrates three rings whose trajectories create on the sphere the sides of the triangle surrounding the axis (fig.1 , fig.2). Puzzle variants Urø and U4/3, where this occurs on their visible surface, are presented in fιg.7 and fig.10. Instead of the fixed supplementary elements 7_n, the visible movable elements of sort III appear in the places corresponding to points A_n. Hereafter, they are referred to as complementary elements 6_π. They are of the shape of a triangle with concave sides and belong to three rings simultaneously. Due to the latter property, there are 1 ,5 times fewer of them than there are elements of sort I belonging to two rings simultaneously and 3 times fewer of them than there are elements of sort Il belonging only to one ring. It results from the fact that the number of elements of all three sorts in one ring is the same in this case. It yields the number of 2n(n-1)/3 pieces, that is, 20 and 8 respectively, which is equal to the number of points A_n on the sphere. The elements 6_n are invisible (fig.17b) if the ring elements cross the arms of the angle 2α_n at a distance from the centre which is different than the surface of the puzzle. A special case occurs when for the asymmetrical ring of the puzzle U4 one visible ring periphery exceeds the arm of the angle 2α₄ and the other one is placed between the trajectory plane t₄ and the other arm of the mentioned angle (the puzzle U4/4 in fig.11) or intersects the angle arm (the puzzle U4/5 in fig.12). In the first case, at points A₄ appear both types of pieces, that is, fixed elements 7₄ and movable elements 64, 4 of each type. In the second case, there occur only 4 complementary elements 6₄. Because of the fact that the rings intersect each other at the angle different from the right angle, the movable elements of sort I are in general of a rhomboidal shape (fig.5, fig.6, fig.8, fig.9) but in the presence of complementary elements 6_n they take on a hexagonal form (fig.7, fig.10) or, if in addition for n = 4 rings are asymmetrical, they assume the shape of an irregular but symmetric pentagon (fig.11). The movable elements of sort Il take on a triangular form (fig.5, fig.7, fig.8, fig.10) or trapezoidal one (fig.6, fig.9). The latter shape appears when the supplementary elements I_n occur in the puzzle. In the case of the rings being asymmetric relative to their trajectories both triangle and trapezoidal elements of sort Il appear in one puzzle (fig.11 , fig.12). If the shape of the puzzle surface is other than spherical, then surfaces of its elements can assume different forms, for example polyhedral. However, sections or projections as well as outlines of their most external visible parts remain as described. As it was already mentioned, the single filling basic elements 3_n. isolated from each other, as well as the single filling supplementary elements 7_n, if the latter occur, remain outside the rings and in the present invention they are immovable. The movable elements are only in the rings and when the puzzle is played with, they slidingly relocate along the rings by rotations of the rings around the centre of the puzzle, as it is indicated with arrows in fig.5 - fig.14, where the immovable filling elements are marked with dark colour. In every full single movement of the ring its elements relocate along the corresponding circle trajectory by the angle ω_n equal to 360/(n-1) degree relative to the puzzle centre. That means that after each turn, the movable elements 5_n of sort I take resting places of the other elements 5_n and the movable elements 4_n of sort Il relocate to resting places of the other elements 4_π. The same concerns the complementary elements 6_n if they occur. In the puzzle Uε the elements 5β can take place of any of 30 intersections Ce on the puzzle surface and in two positions mutually turned by 180 degree. In the puzzle U₄ the elements 5A can take place of any of 12 intersections C4 but only in one fixed position. The number of a freedom degree is lower here. The Il sort elements 4_n belong to the given ring and relocate only within it. Their mutual positioning in the ring does not change. The complementary elements ⁽S₆ permute within all 20 places of the type A₅ in the puzzle Uβ and the elements 64 can occupy only every second place of 8 places of the type A4 in the puzzle IU because they belong to two 4-element subsets and can permute only within the subset. Each two movable elements of the same sort, lying on the opposite sides of the puzzle, are coupled. That means there are n(n-1)/2 permuting pairs of the elements 5_n and n(n-1)/3 permuting pairs of the elements 6_n.

The puzzles presented in fig.5 - fig.12 are selected examples of the puzzle according to the invention and do not exhaust all possibilities. Especially underrepresented are those with asymmetric rings of the puzzle LU. The puzzle construction bases on the central body 1 _n whose outermost parts are the immovable basic elements 3_n and the immovable supplementary elements I_n if the latter occur. The movable elements forming the rings are hooked on the central body and are movably interlocked with each other and with immovable pieces. Fig.16 illustrates an example of the central body 1₆ of the puzzle Ue_/i shown in fig.5, the movable elements 4₆ and 5β shape fitting into it and into each other and the invisible complementary element 6ε together with its modification δβ'. The central body 1ε here consists of a ball-shaped core 11e, 12 radial arms 2% of a pentagonal cross-section sticking out of the core and the visible pentagonal upper parts of the elements 3₆ placed on the arm ends. The evenly distributed basic elements are placed in the same way as the dark pentagons on the surface of a standard football (fig.14). Edges of the arms 2₆ are rounded here so that a circular cross-section of the arm is obtained, which results in linear tangency of the arm 2β with projections of the movable elements and thus reduces the friction coefficient (to illustrate the original shape one of the arms in fig.16 is left unchanged). The visible I sort movable elements 5β of the rhomboidal shape and Il sort movable elements 4₆ of the triangular shape as well as the invisible complementary elements 6₆ fill the space between the arms of the central body in the way shown in fig.17a/17b, thereby creating the complete ball or regular polyhedron depending on whether their visible surfaces remain spherically curved or flat or are of some other shape. When moving, they slide on the surface of the internal core 11β belonging to the central body 1β and on each other's lateral faces and projections (extensions) 8β, 9ε, through which they interlock with the non-movable pentagons 3β and/or with the adjacent movable elements. Spaces between the inner core 11ε and the upper parts of basic elements 3β, surrounding the arms 2₆ of basic elements, as well as spaces under upper parts of the elements 4₆, after assembling, constitute the slots corresponding to projections 8β and 9β. Double sequences comprising the elements 3₆ aligned with the movable elements 4₆ and 5β adjacent to them and to each other form around the puzzle circular corridors (fig.18a), widening at the bottom, along which the rings (fig.18b) slide. Each ring on its bottom inner side has a circular widening projection formed by the lower parts 8β and 9β of the aligned and alternating elements 4₆ and 5₆ respectively. In the described example the ring elements exceed the arms of the angle 2αε in the deeper layer, as a result of which in the places corresponding to points Aβ there appear the invisible movable elements 6₆ whose original shape is close to a spherically curved truncated triangular pyramid (fig.16). While resting the elements 66 belong to the three rings simultaneously and constitute parts of their circular projections (fig.18b). They are not essential from the point of view of the puzzle's logic (they are invisible) and could be removed leaving empty spaces. However to ensure the stability of the other movable elements it is better if the spaces are filled, particularly if they are relatively big. Here (fig.16, fig.17b), to reduce the friction coefficient, the elements 6₆ are rounded up to the point when the shape of the truncated cone 6β inscribed within the pyramid is obtained. Thus they have the role of a roller bearing (in fig.18b they remain in their original shape). If the proportion of the empty space edges is appropriately designed, which results directly from the assumed proportions of the ring elements, it is possible to round the complementary element even to the point of obtaining a ball inscribed within this space.

Fig.20 illustrates a part of a similar solution for the puzzle U4/1 presented in fig.8. In this case, because of the wider rings in comparison with the puzzle U_&i (0₄ > αβ) and twice as low a number of the basic elements 34 being the outer parts of the central body, on which the ring elements hook, and also because of a relatively small size of the basic elements 34, the central body additionally has 8 invisible triangle elements 74 that are joined to the ball 11₄ with the arms 1O₄. Such a solution ensures better interlocking of the puzzle elements. The movable rhomboidal elements 5₄ and movable elements 4₄ in the shape of an elongated triangle attached both under the extensions 12₄ (additional projections) of the quadrangular basic elements 34 and under the invisible triangle elements It, with the help of the extensions 94 and lower parts of the projections 8₄. Fig.20 depicts a part of a circular projection comprising the extensions 124, the supplementary elements 7₄ and the upper part of the projections 84 as well as the lower side fragment of the circular T-shaped groove just below it, which groove is formed at the bottom of the corridor by the slots surrounding the arms 2₄ and IO₄ of the immovable elements and by the lower parts of the extensions 84.

Fig. 22 presents a solution for the puzzle Ue/i (illustrated in fig.5) which is similar to the solution described above. This is an alternative to the solution shown in fig.16. On the surface of the central body, apart from 12 immovable pentagonal basic elements 3₆, there are additional 20 immovable but invisible triangle elements 7₆ joined with the ball 11β of the central body by means of the arms 1O₆. The movable puzzle elements additionally attach under those supplementary elements both when resting and when moving, whereas hardly ever do they interlock with the other mobile pieces. In contrast to the solution presented in fig.16, the circular widening grooves are formed by the parts of the central body rather than by the movable elements.

A problem of size inadequacy of the immovable basic elements belonging to the central body with respect to the ring width, and therefore to the size of the attaching elements, is particularly severe in the case of the rings corresponding to an angle bigger than 2α_n, where there appear complementary elements 6_n that do not touch outer parts of the central body, while resting. The problem can be solved by using an additional layer of grooves and projections, which will be presented in a further part of the description.

A variety of possible solutions as regards the shape of the puzzle elements are illustrated in fig.24 and fig.25, which show a modification of the first approach presented on fig.16 - fig.18b. Here, the movable elements 4β and 5β dig the side parts of their extensions 8β and 9β into the slots of outer fragments 3β of the central body and into the slots of each other. Going further and providing these side parts of the projections and slots with a widening shape (for example dovetail shape) in the direction perpendicular to the widening of the original projection results in a solution where the internal core 11₆ of the central body can be removed while retaining movable interlocking of the puzzle's external elements. In this way the solution with rotating caps separated at both sides of the rings is obtained where all elements of an external puzzle layer are movable. Fig.27 shows elements of such a solution and fig.28 presents their location relative to each other in the resting position. For n = 4 an analogous puzzle with the reverse arrangement of projections and grooves is presented in the publication WO2008026218. Likewise the publication WO2004110575 deals with puzzles of a similar construction. These solutions are recalled here for the sake of easier comparison with the construction of the puzzle according to the invention, which bases on the central body.

The presented solutions involve mechanical assembling of the elements, which requires special shapes of the elements in order for them to be movably aligned and interlocked. Another approach consists in carving corridors of a simple cross-section on the puzzle surface. Simple elements in the shape of rhombuses, triangles or trapezia move along these corridors and are kept in them e.g. with the help of the magnetic field effect. While the shape of the outer visible surfaces of the elements is. in general arbitrary, then good fitting of the surfaces involved in the elements' mutual sliding is essential. Those surfaces will be referred to as sliding surfaces hereafter.

A method of determining initial shapes of the sliding surfaces consists in cutting the external layer of a full or hollow ball or a polyhedron or another compact solid with the help of an open broken (polygonal) line or an open curve line or their combination having both ends on the sphere which contains a puzzle body and whose centre coincides with the puzzle centre. The line will be referred to as the puzzle cutting line or the puzzle generating line L_n. The examples of the generating lines for the construction solutions described above are shown in fig.15, fig.19, fig.21 , fig.23 and fig.26. A cutting process is performed by rotating the generating line L_n that follows a radius vector R whose initial point is in the sphere centre and whose free end runs along trajectories presented in fig.1 or fig.2. The cutting line L_n is included inside the sphere and at any moment of the rotation it lies in a plane perpendicular to the trajectory plane. For n = 6 it is axially symmetrical to the radius vector. The distance between the ends of the generating line L_n on the sphere determines the width of the ring on the sphere. Because trajectories intersect each other and there are 2^*(n-1) intersections on each trajectory, the generating line L_n not only carves circular, mutually intersecting, elongated spaces (corridors) in the outer layer of the full or hollow solid but also cuts the contents of each space, i.e. a ring, into at least 4^*(n-1) smaller elements while carving other corridors. The shapes of the elements obtained in this way, being inside the carved spaces, ideally match each other as well as the shape of the spaces (fig.18a/18b) and it is obvious that they can move along the spaces (after rounding of some edges to avoid their interlocking). To protect elements from falling out during movement, the shape of the cutting line L_n should be selected or designed in such a way as to make it possible to form widening projections and/or grooves, which in turn enables movable digging or hooking of the mobile elements into/onto fragments of the central body and/or into/onto each other. This is not required though in the case of the solutions using the central body where elements are attached in another way, for example with the help of the magnetic field forces. Selection of the appropriate cutting line L_n is simple enough, as its shape represents both a contour of the cross-section of the carved spaces (corridors) and contours of the cross-sections of the mobile ring elements together with the cross-sections of their projections/extensions 8_n, 9_n and/or of slots, all said cross-section perpendicular to the trajectory plane t_π. If the puzzle is not ball-shaped, the generating line L_n should be designed in such a way that at any position its part corresponding to ring projections/grooves be fully included inside the puzzle body.

The above describes only the method of obtaining the initial shape of the sliding surfaces of the puzzle elements and not the way of producing its pieces. To improve movement dynamics of the elements their ultimate shape, described further, slightly differs from the initial one. The advantage of the generating line method is also the fact that it makes it possible to demonstrate different construction solutions for all puzzle types in fig.5 - fig.12 in a quite easy way, which is done below.

In addition to the shape of the generating line L_n and thus the shape of the outline of the cross-sections of the carved spaces (left side of the picture), fig.15, fig.19, fig.21 , fig.23, fig.26 as well as fig.32, fig.33 and fig.34 present also a fragment of the cross-section of the puzzle generated by a given cutting line (right side of the picture). Notation n/x of the generating line refers to the puzzle type created by a given line L_n*. Fig.3 and fig.4 show planes Sβ and S₄, perpendicular to the picture plane, along which the cross-sections of the puzzles Uβ and U₄, respectively, are created. Arrows in fig.3 and fig.4 point both the direction from which cross-sections are presented and the trajectory, perpendicular to the cross-section plane, along which runs the free end of the radius vector of the generating line L_nA shown on the cross-sections. The central body in the right part of the pictures in fig.15, fig.19, fig.21 , fig.23. fig.32, fig.33 and fig.34, unlike the movable elements, is left blank to distinguish it from the mobile pieces. As mentioned above, while comparing both parts of the pictures listed here, it can be easily noticed that the shape of the cutting line simultaneously delineates the cross-section of the central body carvings (left part of the pictures) and the cross-sections (perpendicular to the trajectory plane) of the movable elements together with the cross-sections of their extensions and/or slots (the interior of the cutting line in the right part of the picture).

For a line to be the generating line of the puzzle according to the invention it is essential that its fragments have the right proportion, shape and direction. Yet the most important thing is location of its fragments relative to the arms of the angle 2α_n. If line L_n does not go beyond and does not touch the arms of the mentioned angle at some level (fig.19, fig.21 , fig.34), then the supplementary elements 7_n appear at this level in the places corresponding to points A_n (to axes a_n). In fig.19 and fig. 21 they are invisible. If the cutting line ends are allowed to be located at a smaller distance from each other and thus to determine an angle smaller than 2α_n (fig.30, fig.31 , fig.34), then the mentioned supplementary elements 7_n become visible, as illustrated in fig.6 and fig.9 and as it is shown on the cross-section in fig.34 (right side of the picture). In the opposite case, i.e. when line L_n exceeds the arms of the angle 2α_n (fig.15, fig.23, fig.26, fig.32, fig.33, fig.35, fig. '36, fig.43 and fig.44) in some distance from the puzzle centre then the complementary elements 6_n belonging simultaneously to three rings appear at this level in the places corresponding to points A_n. In fig.32, fig.33, fig.35 and fig.36 they are visible, constituting additional elements of the outer logical puzzle layer, because the cutting line ends are located beyond the arms of the angle 2α_n. Optimal solutions are obtained when the cutting line L_n, at any level r, crosses the circle with radius r and centre O_n at most twice. The generating line in fig.26 does not fulfil this requirement (left side of the picture) because of the necessity to form widening projections enabling dovetail digging of the elements into other adjacent movable ones. It causes the appearance of several dozen small movable remnant elements 13 and 14, in the shape of tetrahedrons in this case (fig.27), which should be removed. A similar situation takes place in the case of line L_n illustrated in fig.29. This one creates a puzzle where movable elements form a widening circular groove on the undersides of the rings and where the central body corridors of a simple shape in the middle of their floor have a widening circular projection (rail) onto which the movable elements hook. Because of a considerable number of the remnant pieces (above one hundred in this case), both the circular projections of the corridors and sides of the circular grooves of the rings have a series of holes and breaks which are leftovers of the removed remnant elements. Such solutions give much worse mutual fitting of the puzzle elements.

Fig.7 and fig.10 present puzzles of the widest rings, where ring elements exceed the arms of the angle 2α_n at the level of the puzzle surface. While resting, the visible complementary elements 6_n are not interlocked with the outer parts of the central body but only with the other movable elements. Additionally, the wide rings cause size reduction of the visible fragments 3_n of the central body. There may be a justified fear for small stability of such a solution and, in the presence of a clearance, for possible falling out of the elements, particularly in the case of the puzzle U4/3 presented in fig.10, where proportions between the visible fragments of the immovable puzzle elements and the movable ones are extremely inadequate. Fig.33 and fig.35 show a way of elimination of such risk respectively for the puzzle Uεra in fig.7 and for the puzzle U_4/3 in fig.10. Fig.33 presents modification of the not very stable solution in fig.32. In both cases the additional layer of the projections/grooves is introduced under the assumption that the elements of the puzzles shown in fig.6 and fig.9 are best interlocked, as their rings are most narrow. Therefore in the lowest layer Wi (the added layer of projections/grooves) the fragments of the central body and the bottom parts of the movable elements create equivalents of the puzzles, respectively, U₆/2 in fig.6 and U4_/2 in fig.9 (as for example that one whose generating line is marked with a dotted line in fig.30) and this layer of the puzzle is treated as a basic layer of the projections/grooves. On the top of the elements constructed in this way two supplementary levels are added, which first create the forms of the puzzles Uε/i in fig.5 and U4/1 in fig.9 (the equivalent in fig.19) in the higher layer W₂ and which then in the highest visible layer W3 form the puzzles Uβ/₃ in fig.7 and U4/3 in fig.10 with the wide rings, where the movable complementary elements 6_n can attach under the rest of the elements, which now are well interlocked in the lower layers. Here the widening of the original circular projection creates two parallel simple projections running along the sides of the ring. All puzzle elements apart from the visible pieces 6_n and the invisible pieces 7_n are here two-level. It is clearly demonstrated in an example of the basic element 36 in the right part of the fig.33, where the levels are separated with a dotted line. The lower level of the element is equipped with an additional extension 12β.

The generating lines of the puzzle LU, where the rings are asymmetric relative to their trajectories, are obtained by joining halves of two different symmetric cutting lines. For example the puzzle U4/4 illustrated in fig.11 can be obtained by the combination of the halves of the generating lines of the puzzles in fig.9 and fig.10 at appropriately selected proportion. Similarly the puzzle U4/₅ shown in fig.12 is obtained through the combination of the halves of the lines generating the elements of the puzzles in fig.8 and fig.9. The example of its generating line L₄/5 is presented in fig.37.

The sliding surfaces of the elements of the puzzle according to the invention, determined with the method of the generating line, are mostly parts of conical or spherical surfaces. To limit friction of sliding movement it is advantageous to replace some of the adjacent conical concave surfaces of the elements or/and spherical concave surfaces of the elements with flat surfaces or concave surfaces but with a different curvature radius or to eliminate some faces (an empty element) altogether, thus enabling movement only on the edges of the neighbouring faces. Some of the adjacent convex surfaces of the elements, on the other hand, could be made slightly more convex, however it is enough to modify the curvature slightly only on one of the two adjacent surfaces. This leads to replacing surface tangency of parts of element faces with their linear or point tangency. All edges of puzzle elements that are essential for movements (that is, lines of the intersections of parts of sliding surfaces) should be appropriately rounded to eliminate their mutual interlocking (collision) during movement. This rounding may even lead to a shape change of the solid part whose edges are rounded, for example a change of the regular pyramid into a cone or a ball inscribed within the pyramid etc. Thickness of the puzzle's outer logical layer as well as thickness of its internal layers is arbitrary, however they should be optimized with respect to the friction coefficient and stability of the elements, which to a certain extent depend on the material the puzzle is made of. An appropriate selection of the generating line, and thus the shape of the puzzle elements, may also lead to an optimal distribution of the forces affecting the sliding surfaces. While in the case of the puzzle Uβ the cutting line must be symmetric relative to the trajectory plane, the elements obtained may be partially deprived of symmetry as long as it has no negative effect on their mutual fitting and movement dynamics.

To ensure bigger precision of rotation and at the same time to protect against mutual blocking of the movable elements (in order to commence the rotation, all the rings must be in their proper position), it is advantageous to equip the puzzle with stopping means enabling the movable elements to click into resting positions after a full, finished rotation of a ring. The best location for these stopping devices is on the surface of the internal core 11_n exactly at the points C_n of the trajectory intersections, because it is the precise positioning of the elements of sort I which is most essential here. An example of such stopping devices are small balls on springs, placed in small holes on the surface of the core 11_n, fully hiding during movements of the elements and jumping, after ending of the ring movement, into shallow suitable hollows made on the undersides of the elements of sort I. In turn, to provide more tight alignment of the elements and at the same time to prevent them from jamming during rotation, it is advantageous to join the outer elements 3_n (and I_n) of the central body with its internal core 11_rt in such a way as to provide a certain minimal flexibility of the connection, for example by a springy joint shown in fig.38. The springy joining of the most external upper parts of the filling elements 3_n and I_n with their arms 2_n and 1O_n respectively is another alternative solution. In any approach the springy element should exert just the right pressure to hold all the pieces in place while giving enough flexibility for a smooth rotation. The matching hole and plug on the joint should be in the angular shape and long enough to prevent the element from pivoting and tilting. The springy joints are applied to the immovable pieces of the puzzle whose movable elements do not interlock with them (fig.29).

On the spherical surface of the puzzle according to the invention it is quite natural and easy to delineate geometric figures corresponding to the faces of regular polyhedrons. Fig.39a, fig.40a and fig.41a present the puzzle Uβ_/1 (fig.5) having on its surface the drawn edges of the polyhedrons whose spherical faces can be covered with different colours or patterns. If some vertices of such faces are left on the sphere and the spherical surfaces between them are transformed into a flat shape, then the puzzle in the shape of the polyhedron will be obtained. This requires that the projections/grooves be designed at an appropriately deep level relative to the external circumsphere. Thus, when any two closest points B_n are joined pairwise by a line, then for n = 6 a regular icosehedron Uβ_/i_A (fig.39a/39b) and for n = 4 a regular octahedron U4/1A (fig.45) are obtained. The symbol A means that the polyhedron is tangent to the inscribed sphere at points A_n. Symbols B and C have analogous meanings for the subsequent puzzles. The puzzles illustrated in fig13 and fig.14 are transformed to a polyhedral shape by leaving the vertices of the basic elements on the sphere and flattening all spherical surfaces between them (fig.39c) or by leaving the vertices of the basic elements and of all triangle elements on the sphere. When each pair of the closest points A_n is joined by a line then a regular dodecahedron U_6/IB (fig.40a/40b) and a regular cube U4/2B (fig-46), whose faces have basic elements 3_π in their centre, are obtained for n = 6 and n = 4 respectively (for n = 4 the puzzle U4/2 is recommended as a basic one because in other cases the elements 3₄ are reduced to null in flattening operation). When the points C_n are joined to each other then the pictures presented on the surfaces of the balls in fig.1 and fig.2 are obtained or, after flattening, the polyhedral equivalents of such solids. When each point A_n is joined by lines with the closest points B_n then for n = 6 30-hedron Uβ_/ic (fig.41 a/41 b) and for n = 4 spherical or polyhedral 12-hedron U₄/ic (fig.47), whose all faces are identical rhombuses, are obtained. The vertices of the spherical rhomb are not included in the same plane, therefore to transform a shape of the figures from spherical to flat one, the rhomb vertices corresponding to points B_n should be left on the sphere and the ball-shaped puzzle surface should be truncated by planes that include the longer diagonal of the rhomb and are parallel to the shorter diagonal. Still another solution is obtained when on the surface of each rhomboidal element 5_n of sort I four right triangles are distinguished by its diagonals. Then each ring consists of a chain of 2(n-1) identical, alternately placed pentagons or hexagons. By giving the same colour or pattern to all figures belonging to a given ring n rings are distinguished, each having a different colour (fig.42). In the latter case the puzzle keeps its spherical shape.

For polyhedral solutions, in order to keep an equal width of the rings and actually to eliminate arcs that appear when conical surfaces intersect flat faces of the polyhedron, it is necessary to replace the conical surfaces with plane ones at least at the level of the intersections. This is achieved in the following way: the fragments of the generating line L_n should run parallel to the radius vector R (i.e. parallel to the trajectory plane t_n) at least along a certain segment within the space between the spheres circumscribed around and inscribed within the polyhedron. For the puzzles U&IA, Lbie it is illustrated in fig.43 and fig.44 whereas for the puzzle U₄^B - in fig.48. If the supplementary/complementary elements are not supposed to be visible then the mentioned parallel segments of the generating line L_n should intersect the arms of the angle 2α_n at the place where the polyhedron surface intersects the axes a_n (fig.43., fig.44). In fϊg.43, fig.44 and fig.48 the surface of the polyhedron is denoted by symbol P with appropriate index that indicates the puzzle type. A shaded part of fig. 48 shows a fragment of the cross-section of the central body of the puzzle U4/2B and its external elements 34 and 7₄. The generating line U/IB illustrated in fig.44 exceeds the arms of the angle 2αβ at two levels and thus it will generate two sets of the complementary elements. The first one is at the level of the projections/grooves, and these elements can be retained or removed, mainly depending on their size. The second set is directly under the puzzle surface and consists of the elements in the shape of small and narrow pyramids. The latter elements, even if retained, will fall out anyway when the ring is in the position exactly in-between its two resting positions, because the elements emerge uncovered then.

The above examples do not exhaust all possibilities. It is feasible to put on the puzzle surface any arbitrary pattern, for example the globe, or some picture or to give it any arbitrary shape or texture. The logic of the puzzle is such that the design visible on its surface is disturbed by several random movements of the rings. The task consists in restoration of the original order by intentional displacing of the movable puzzle elements through sequential rotations of the rings.

The puzzle according to the invention differs from the existing solutions with rotatable rings in that its rings of the movable elements intersect each other at untypical angles other than the right angle in spite of the fact that only two rings meet in each intersection. It also causes that besides the triangular shape the puzzle elements take on untypical rhomboidal shapes and, in special cases, trapezoidal, pentagonal or hexagonal ones. In comparison to puzzles with typical perpendicular or latitudinal/longitudinal rings the puzzle having four or six equivalent ring axes can be perceived as a big challenge for human mind accustomed to Cartesian rectangular coordinate system and to natural perpendicular world directions. The puzzle differs from spherical or polyhedral versions of Rubik's puzzle in that the group of the elements subject to relocation in a single movement, that is the ring versus the layer, is more numerous (20 to 11 for lie and 12 to 7 for U4), and in addition the rotation of one ring disturbs all the other rings without exception. Only the tetrahedral version of Rubik's puzzle has such a quality. Taking into account coloured faces of the puzzle Uβnβ (fig.40a, fig.40b) corresponding to dodecahedral Rubik's puzzle or of the puzzle U_4/2B (fig.46) corresponding to basic Rubik's cube, the ring rotation disturbs 10 among 12 pentagonal faces of the puzzle Uβnβ or all of 6 square faces of the puzzle U4/2B, whereas in Rubik's puzzles only 5 among 12 and 4 among 6 faces respectively (the rotating group is not disturbed). All of it makes the puzzle according to the invention more complex in abstract terms though it does not really increase the number of permutations of its elements. Construction of the puzzle is another quite essential difference. The groups of the movable elements rotate around the puzzle centre whereas in Rubik's puzzle they rotate around the axes going through its centre. In addition, the outer elements of the central body do not pivot here.

Compared to the solutions with rotating caps presented in WO2008026218, EP0874672 or WO2004110575 their analogues represented by the puzzle with rotating rings give in fact fewer possible permutations yet it can be partially balanced by a smaller number of freedom degrees of the movable elements, which makes it more difficult to put them into a desired stage. Actually in view of such a big number of the elements (about one hundred in puzzle U₆), a lower number of permutations is rather a merit than a drawback, as it makes the puzzle solvable for a bigger number of potential players. As it was described above, the width of the rings in the puzzle according to the invention is within some range favourably arbitrary and in the version containing four rings they are allowed to be asymmetric. It increases the number of the possible puzzle versions. The solution having the central body ensures closer fitting of the puzzle elements in comparison to solutions with rotating caps, where, as it was shown in fig.27, widening projections and grooves result in occurrence of several dozen to even above two hundred remnant elements that should be removed. Remaining holes and channels, and particularly their edges, increase the possibility of element interlocking (colliding). The puzzle according to the invention has definitely better proportion of the extensions/slots relative to the size of the elements. Its bigger projections allow for bigger rounding of element edges, which favourably improves the movement dynamics of the elements, protecting them against mutual interlocking during rotations. Moreover, their smooth surface is an undeniable advantage. In addition, the latter feature allows for slight changes of the curvatures of elements' faces, which essentially reduces the friction coefficient. And the last but not least advantage of the solution with rotating rings in comparison to solutions with rotating caps is that it enables flexible fitting of the elements. The springy joints of the outer elements of the central body with its internal core 11_n enable dynamic local adjusting of the circular groove to the circular projection of the ring during rotation.

The application of the generating line method allows for huge freedom in designing shapes of the puzzle elements and the number of the possible solutions here is virtually unlimited. It concerns not only the puzzle with rotating rings but can be used more widely, for example in designing puzzles with rotating caps (fig.26, fig.36). The cutting line method can be applied in different types of computer software supporting engineering work.

The biggest advantage of the ball-shaped puzzle Ue with the ring width corresponding to an angle 2α_n amounts to the fact that it has elements of quite regular visible surfaces forming the design corresponding to the standard football.

Realization of any version of the invention can help develop spatial imagination and ability of logical thinking of children and teenagers. It can be a source of amusement for everybody who likes logical challenges. The level of abstraction is very high here because of the puzzle shape and because of the ring location in planes that are not perpendicular to each other. The particular case of the solution in the shape of the football can be an excellent gadget during world or European football championships or could become a symbol of some football team, a famous club, some football association or organisation.

Claims

C I a i m s

1. A three-dimensional puzzle comprising a plurality of shape fitting pieces a part of which are movable and relocated through sliding movements consisting in rotations of groups of elements around the axes intersecting the puzzle centre, characterized in that a puzzle external surface of an arbitrary shape is included between two spheres having centres in the puzzle centre and puzzle movable elements of at least two different shapes are arranged in n = 6 or 4 identical mutually intersecting rings that run, respectively, according to six (fig.1) or four (fιg.2) circles constituting circular trajectories for the rings; said circles are determined by lines of intersection of a sphere, concentric with the puzzle, with planes passing through the sphere centre parallel to faces either of a regular dodecahedron circumscribed on the sphere or of a regular octahedron circumscribed on the sphere respectively; in addition the elements of the ring, in any plane running through the puzzle centre and perpendicular to the plane (t_π) of the ring trajectory, are fully included between arms of an acute angle (2β_n) which is symmetrical relative to the plane (t_n) and whose vertex lies in the puzzle centre, where in turn (β_π) is an angle between trajectory plane (t_n) and sphere axes (b_n) passing through the central points of, respectively, pentagonal or quadrangular figures determined on the sphere by ring trajectories, where empty spaces that occur between rings around the axes (b_n) are filled in with additional single basic elements (3_n) in the number of 3(n-2) pieces, whose outlines of visible surfaces for n = 6 are pentagonal and for n =4 are quadrangular and which are immovable and wherein sliding relocation of movable elements is performed through sequential rotations of rings around the puzzle centre by an angle of 360/(n-1) degrees along corresponding trajectories, moreover the puzzle comprises at least 3n(π-1) movable elements among which π(n-1) ones constitute visible elements (5_n) of sort I in resting position taking places of trajectory intersections (C_n) and 2n(n-1) ones constitute visible elements (4_n) of sort Il in resting position fitting tight to sides of basic elements (3_n) and each ring includes at least 4(n-1) movable elements but at most 2(n-1) movable elements of the same sort.

2. A puzzle according to claim 1 , wherein the puzzle surface is in a shape of a sphere or of a polyhedron.

3. A puzzle according to claim 1 , wherein in resting position the ring edges visible on the puzzle surface intersect the sphere axes (a_n) passing through the centres of triangle figures determined on the sphere by ring trajectories whereby the outlines of visible surfaces of said I sort elements (5_n) take on a rhomboidal shape and the outlines of the visible surfaces of said Il sort elements (A_n) take on a triangular shape.

4. A puzzle according to claim 3, wherein two complementary figures in a shape of an acute-angled triangle are distinguished on the visible surface of each of said movable I sort elements (5_π) thereby revealing 2n(π-1)/3 hexagonal figures on the puzzle surface (fig.13, fig.14).

5. A puzzle according to claim 4, wherein in the case of n = 6 one of 5 or 10 or 20 and in the case of n = 4 one of 4 or 8 different colours or patterns are marked on each of said hexagonal figures whereby each of said movable elements of sort I is two-coloured and each of said movable elements of sort Il is uni-coloured.

6. A puzzle according to claim 1 , wherein depending on the width of the visible ring surface and for n = 4 also on ring symmetry there appear additional movable complementary elements (6_n) and/or additional immovable supplementary elements (7_n), the latter filling empty spaces between rings, and wherein the outlines of visible surfaces of said elements in both kinds take on a triangular shape, the outlines of the visible surfaces of said I sort elements (5_n) take on a rhomboidal or hexagonal or pentagonal shape and the outlines of the visible surfaces of said Il sort elements (4_n) takes on a triangular or trapezoidal shape or half of them triangular and half of them trapezoidal one.

7. A puzzle according to claim 1 , wherein there occur said additional elements (6_n) and/or (J_n) which are invisible.

8. A puzzle according to claim 1 comprising a central body (1_n) and elements of rings which are shape fitted to each other and to carvings of the central body, which carvings run along said trajectories in fig.1 or fig.2.

9. A puzzle according to claim 8, wherein movable interlocking of the ring elements with the central body as well as capability of sliding rotations of the ring around the puzzle centre are provided by circular projections and/or grooves which on sides or/and on undersides of rings are formed by sequences of, respectively, projections/extensions (8_n), (9_n) and/or slots of consecutively aligned movable ring elements (fig.18b), and by circular grooves and/or projections of the corridors (fig.18a, fig.20), corresponding to them, which are formed by aligned sequences of the movable elements and the outer elements of the central body, thereby enabling the rings to be slidingly dovetailed with the said corridors formed by other elements of the puzzle.

10. A puzzle according to claim 9, wherein there occur more than one layer of corresponding grooves and projections.

11. A method of determining an initial shape of sliding surfaces of elements of a puzzle according to claim 8, 9 or 10, wherein it consists in rotations of a generating line (L_n) which is an open broken (polygonal) line or an open curve line or their combination included inside sphere and having both ends on the sphere and which follows a radius vector (R) whose initial point lies in the sphere centre and whose free end runs along said trajectories on the sphere and where for n = 6 the line (U) is axially symmetric relative to a radius vector (R); where the said generating line (L_n) is the same for each of n trajectories and lies in a plane crossing the sphere centre perpendicular to a trajectory plane (t_n) and is included between arms of an acute angle (2β_π) with its vertex at the sphere centre and with its arms symmetric in relation to said trajectory plane (t_n); where the said generating line (L_n), while rotating, cuts a full or hollow solid concentric with the sphere and included inside the sphere, thereby determining the sliding surfaces of the carvings of the central body and sliding surfaces of the movable elements shape fitting thereto, and in addition to which a shape of the generating line (L_n) simultaneously reflects contours of cross-sections of the carved spaces (corridors) as well as contours of the cross-sections of movable ring elements along with cross-sections of projections/extensions and/or of slots of said elements filling the carved spaces, all said cross-sections being perpendicular to said trajectory plane (t_n).

12. A puzzle according to claims 8, 9 or 10, wherein the shape of non-sliding surfaces is arbitrary and initial shape of sliding surfaces determined with a help of the method according to claim 11 is slightly modified, that is, edges of the movable elements and of the central body, essential from a point of view of movement fluidity and resistance and resulting from mutual intersecting of fragments of sliding surfaces, are rounded up, even to achieving a full change of geometrical character of a part or whole of element solid and/or where for the purpose of decreasing friction coefficient the surface tangency of element faces are replaced with linear or point tangency through slight changes of curvatures of some fragments of sliding surfaces or through elimination of such fragments and/or where initial symmetry as well as tight fitting are not fully retained.

13. A puzzle according to claim 8, wherein at least some of puzzle elements are equipped with stopping means enabling movable elements to click into determined resting positions after each full and finished ring rotation by an angle of 360/(n - 1) degree.

14. A puzzle according to claim 9, wherein immovable elements (3_π) and/or (7_n), if the latter occur, are assembled with an internal core (11_n) of said central body (1_n) or with their own arms (2_n), (1O_n) with the help of springy joints.

15. A puzzle according to claim 2, wherein its polyhedral surface is inscribed within the sphere or circumscribed around the sphere and wherein the ring edges on the polyhedral faces are rectilinear.

16. A puzzle according to claim 1 , wherein the puzzle external surface is covered with any design, pattern, geometrical figures or a set of colours or where any texture is given to the visible faces of the puzzle elements.