AU2002313996B2 - Magnetic geometric puzzle - Google Patents

Description

MAGNETIC GEOMETRIC PUZZLE BACKGROUND OF THE INVENTION Using permanent magnets as a method of connecting together toy pieces is well known. Permanent magnets are a popular choice as a connection between pieces because they form a quick and easy connection.

Toys with geometric shaped pieces which are connected together with permanent magnets are also known, for example US 6,017,220 (SNELSON) and US 5,009,625 (LONGUET-HIGGINS). Both of these relate to toys rather I0 than puzzles, the distinction being puzzles have a defined goal.

The magnetic blocks in Snelson are essentially flat pieces. In one embodiment (figure a number of identical pieces that connect together to form a uniform convex polyhedron (an octahedron). Each piece however, is contains more than one vertex of the octahedron.

The magnetic blocks of Longuet-Higgins are of three-dimensional form. The blocks are either Block B or Block Y form (figures 1 and The blocks can be joined to form a variety of interesting shapes such as the rhombic triacontahedron (in figure 10) which is the dual of the icosidodecahedron.

Both block types (block B and block Y) are needed to construct the rhombic triacontahedron. Furthermore, the vertices of the rhombic triacontahedron are not uniform.

Geometric puzzles with magnetically connecting pieces are also known, for example US 3,655,201 (NICHOLS) and US 4,886,273 (UNGER). Both patents disclose puzzles which comprise: a number of identical pieces, each piece having magnets embedded in the faces thereof such that pieces can be connected (by magnetic attraction) to form a cube.

US 3,655,201 (NICHOLS) discloses eight cube-type pieces magnetically engaged to form a larger cube. The object of the puzzle is similar to a Rubik's 2 Cube®, that is to rotate planes of the cube-type pieces to arrange the faces of the cube.

US 4,886,273 (UNGER) and US 5,127,652 (UNGER) disclose a reversibly breakable puzzle. The pieces are identically shaped and are connected by magnetic attraction to form a ball. In different embodiments the pieces form a cube and a pyramid.

Neither Nichols or Unger disclose or fairly suggests the solid to be to constructed of identical pieces that form relatively complex shapes of the uniform convex polyhedron solid form other than cubic.

It is considered that a puzzle with pieces that form 'complex' shapes such as a truncated icosahedron is more interesting than the relatively rudimentary cube. The Unger cube design has only 8 pieces, each piece having a 'familiar' shape whereas in the truncated icosahedron of the present invention, there are 60 pieces which are of an 'interesting' shape.

SUMMARY OF THE INVENTION zO The present invention is a magnetic geometric puzzle comprising pieces having magnets embedded in the faces of the pieces. The pieces are designed by dissecting an original form into a number of identical pieces. The goal of the puzzle is to connect the pieces together using the magnetic attraction to construct the original form. The original form is chosen from the Z 5s set of objects known as uniform convex polyhedra.

A uniform polyhedron is a geometric form that has identical vertices, of which there are eighty such forms.

A'globally' convex (hereafter simply convex) polyhedron is a shape that has all vertices further from the centre than any point on the local faces or edges.

Stated another way, a convex polyhedron is a solid without any 'indented' faces or vertices.

A uniform convex polyhedron is a shape with identical vertices and convex form. There are only eighteen forms that match the criteria of being uniform convex polyhedra, see Table 1.

S A good reference for uniform polyhedra can be found at: http://mathworld.wolfram.com/UniformPolyhedron.html Table 1: List of uniform convex polyhedra and their duals: Uniform Convex Polyhedra Corresponding Dual of Uniform Convex Polyhedra tetrahedron tetrahedron truncated tetrahedron triakis tetrahedron octahedron cube cube octahedron cuboctahedron rhombic dodecahedron truncated octahedron tetrakis hexahedron truncated cube triakis octahedron small rhombicuboctahedron deltoidal icositetrahedron truncated cuboctahedron disdyakis dodecahedron snub cube pentagonal icositetrahedron icosahedron dodecahedron dodecahedron icosahedron icosidodecahedron rhombic triacontahedron truncated icosahedron pentakis dodecahedron truncated dodecahedron triakis icosahedron small deltoidal hexecontahedron rhombicosidodecahedron truncated icosidodecahedron disdyakis triacontahedron snub dodecahedron pentagonal hexecontahedron Geometric construction of pieces: The dissection is performed by 'slicing' the uniform convex polyhedron at the mid-point of each edge, slice made in a plane, said plane is orthogonal to the edge; each dissection face bounded where adjacent dissection planes intersect.

Another (equivalent) way of stating the above is each dissection plane that contains the one edge of the uniform convex polyhedron's dual and the centre of the solid; dissection faces being dissection planes bounded by the intersection of adjacent planes.

Another (equivalent) way of stating the above is the dissection faces are formed by the surface that contains the following points: the centres of two adjacent uniform convex polyhedron faces, the mid-point of the edge common to the two said faces, and the centre of the solid.

Each piece is a convex solid bounded by dissection faces and sections formed by the dissections of the surface of the original solid.

To dissect a sphere in the claimed manner, consider a uniform convex polyhedra solid dual inscribed in the sphere. Now consider the planes containing a dual edge and the sphere centre. It is the intersection of the adjacent planes that form the boundaries of the dissection faces. The result is a number of identical wedge-shape pieces. Each dissection face of each wedge-shape piece has a magnet embedded in it.

The spherical embodiment of the invention is essentially a 'rounded' version of the uniform convex polyhedron, ie the dissection faces are the same as in the dissected uniform convex polyhedron with the outer surfaces Definition of terms: A graph is a mathematical object that contains vertices and lines between the vertices called edges. A polyhedron can be mapped to a graph, and this is called a Schlegel graph. This is useful so that the (non-spatial) information is represented in two-dimensional form.

A Hamiltonian circuit is a continuous path loop on a graph that visits each node exactly once.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a completed puzzle according to the present invention.

Fig. 2 is an individual piece of the puzzle of the present invention.

I 0 Fig. 3 is a design for an individual piece of the present invention.

Fig. 4 is a Schlegel graph representing the orientation of magnets of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS iS Figure 1 shows a truncated icosahedron puzzle according to the present invention, with the pieces slightly separated for dramatic effect. The three outer faces of each piece can be seen clearly. A small part of the dissection faces of the pieces can also be seen. Two of the three outer faces of each piece is a sixth of a hexagon, while the other outer face is a fifth of a 2.o pentagon.

Figure 2 shows an individual piece of the puzzle in figure 1, with outer faces on the top of the figure and two of the dissection faces on the sides. The circles on the dissection faces are the exposed surfaces of the embedded cylindrical magnets. The acute point at which the three dissection faces would meet is absent; when the pieces are connected together the result is a 'hollow' truncated icosahedron.

It is important to note the 'hollow' refers to the inside of the truncated 39 icosahedron when completed, not to the individual pieces. The individual pieces may themselves be hollow depending on the material and method of manufacture.

The advantage of hollowing the solid is that the sharp vertex where dissection faces meet is absent. Manufacturing the piece in this way removes an acute point and leads to the following advantages: easier to manufacture, safer, and less prone to breakage.

Geometry of a truncated icosahedron: A truncated icosahedron is formed of 20 regular hexagons and 12 regular pentagons.

Let edge length of hexagons and pentagons be'a'.

Centre of truncated icosahedron to centre of hexagonal face: 2.267a Centre of truncated icosahedron to centre of pentagonal face: 2.327a Dihedral angle between hexagon-hexagon: 1420 37'= 142.60 Dihedral angle between hexagon-pentagon: 1380 11'= 138.20 IS From these facts, the design of the pieces can be easily derived.

Figure 3 shows the design of six of the seven faces of the puzzle piece in a 'flattened-out' form, where lengths are in millimetres. The puzzle with pieces of dimensions given in figure 3 has a diameter of approximately 10cm when 2, pieces are put together. The embeded cylindrical magnets have diameter of 6mm and a depth of 3mm.

The large circles in the 3 faces at the bottom of the figure are a construct in determining the 'centre' of each face. These large circles 'just touch' are tangential to) three of the face's edges. The smaller circles are concentric to the larger circles and represent the placement of the embedded cylindrical magnets.

Embedding the magnets in the dissection faces can be described in the ,3O following concise manner: SEach piece is adjacent to three other pieces (where adjacent means having dissection faces touching). Two dissection faces comprise the edge of a hexagon and a pentagon one dissection face has the edge of two hexagons the orientations of the magnets on a piece is labelled clockwise from the h-h piece, where clockwise direction is looking in plan view with vertex at the top.

The pole of the magnet on each dissection face is either north or south S an arrow pointing away from a vertex is designated North, an arrow pointing towards a vertex is designated South.

The 60 pieces can be numbered in the following manner: the vertices are consecutively numbered around a Hamiltonian circuit formed on the truncated icosahedron.

Referring to figure 4, consider the piece numbered 7 and the adjacent pieces are numbered 15, 8 and 6 with magnet poles N, S and N and facing outwards to each of these pieces respectively, with 15 being the h-h face, 8 and 6 being the h-p faces clockwise from the 15; the arrangement of the magnets in this piece when in relation to other pieces (when puzzle is solved) are described concisely by the syntax: 7: (15N, 8S, 6N) The piece on its own is simply: 0 7: NSN Figure 4 shows the 'vortex configuration' of magnet orientations, so called since the arrows all point in a clockwise and inward direction resembling a vortex.

The orientation of magnets has been chosen such that each piece has at least one north and one south magnet pole facing out of the piece. Thus there are 6 possible magnet configurations, and hence 6 different piece types (since the NNN and SSS do not fit the criteria of at least one north and one JO south pole facing outwards): SSN, SNN, NSN, SNS, NSS, NNS.

The 'vortex configuration' gives leads to 10 of each piece type as shown in Table 2.

Table 2: Magnet orientation Piece number SSN 1 2 31 32 33 8 14 24 43 54 SNS 4 19 38 35 49 57 16 27 41 52 SNN 5 20 39 46 50 56 15 23 42 53 NSS 6 21 26 45 51 59 18 29 36 48 NSN 7 22 25 44 55 58 17 28 40 47 NNS 3 30 37 34 60 9 13 12 11 (O Method of manufacture: The geometric puzzle of the present invention could be made in a number of ways, which would be obvious to a person skilled in the art depending upon the material used. For example, if plastic were used an injection mould technique would be appropriate, if solid aluminium were used then CNC 1' milling and drilling would be appropriate.

Each piece is made with a hole on each dissection face; the hole either made at the same time as the faces of the pieces or drilled after the piece is formed, depending on the material and method of manufacture. A magnet is then tL inserted into each hole and stuck with adhesive. The magnet is preferably tightly fitting in the hole.

Alternatively, if the piece were made out of a settable material, the magnets could be placed in the piece while it sets. For example, the magnets could be attached (with magnetic attraction) on the walls of a mould. A settable compound such as epoxy would fill the mould, and when the settable compound had hardened, the piece could be removed with magnets set in place.

The magnets are of sufficient size and strength such that the puzzle holds together under the force that gravity. The magnet made of neodymium iron boron or ferrite could be used.

To play with the toy, the pieces are first separated from each other. Then the player connects pieces together. The player continues to construct and deconstruct pieces until the complete solid is formed. Although putting together a number of identical pieces to form a uniform polyhedral solid may Sseem, prima facie, fairly easy, but once the magnet polarities are taken into account the puzzle becomes much more difficult. Hence a player may need to experiment to discover a solution.

Optional features: t'9 In one embodiment the dissection faces of the geometric toy are coloured or marked, to represent the orientation of embedded magnet.

In another embodiment the outer surfaces of the pieces has designs such that when the solid is constructed a larger tessellation or design is formed. For example, an approximated atlas of the world could be formed on the surface of the dissected polyhedron or dissected sphere. Alternatively, a design that would typically be found on a soccer ball could be used.

The geometric toy could be constructed of any suitable material including, but Lo not limited to: glass, wood, plastic, aluminium or ceramic. The material is preferably non-ferromagnetic.

In one embodiment the geometric toy is constructed with the pieces separated by rods, i.e. rods are placed between the magnets on dissection faces. The S construction of puzzle would result in a cage-like structure. The rods could be made out of a ferromagnetic material (such as iron) or the rods could themselves be magnets.

It would be impractical to elaborate on the detail of all uniform convex polyhedra dissection, however the general algorithm is given: Determine the shape and important dimensions (edge length, dihedral angle between faces and the inscribed sphere radius (or radii), which can be found at 'Mathworld' cited above).

Isolate the various face combinations (eg. for truncated icosahedron: hexagon-hexagon and hexagon-pentagon) and determine the dimensions of dissected pieces using basic geometry.

Magnet orientations are chosen arbitrarily but consistently such that S all pieces fit together with every north pole having an appropriate south pole on a matching face).

Claims (4)

1. A geometric puzzle formed by the dissection of a solid where said solid is any uniform convex polyhedron solid (other than a cube); said solid dissected into a number of identical pieces such that each piece contains exactly one vertex of said solid, characterised by each face created by the dissection has a magnet embedded in it.

2. The geometric puzzle of claim 1 where said dissection faces are formed by the planes bounded by the following lines: the lines that extend from the centre of said solid to the centre of two adjacent faces of the solid, the lines that extend from the centres of the said faces to the mid-point of the edge common to the two faces.

3. The geometric puzzle in claims 1 or 2 where the solid is a truncated icosahedron.

4. The geometric puzzle sustantially as herein before described with reference to the description and drawings.