US3665729A

US3665729A - Cut ornamental gem

Info

Publication number: US3665729A
Application number: US24225A
Authority: US
Inventors: Maximo Elbe
Original assignee: COLORANT SCHMUCKSTEIN GmbH
Current assignee: COLORANT SCHMUCKSTEIN GmbH
Priority date: 1969-04-01
Filing date: 1970-03-31
Publication date: 1972-05-30
Anticipated expiration: 1989-05-30
Also published as: ES378104A1; IL34087A; GB1299319A; SE378506B; JPS542147B1; AT321010B; IE33758B1; IE33758L; NL7004257A; CH521728A; DE1916643A1; SU449464A3; BE747529A; CA941175A; DE1916643B2; FR2042156A5; IL34087A0; DE1916643C3; LU60550A1

Abstract

A diamond is cut to have optically cooperating first facets defining substantially the angle of dispersion so that light rays transmitted through the cooperating facets are dispersed. Second optically cooperating facets are also provided which define half the angle of dispersion so that reflected light impinges a facet at the angle of dispersion so that reflected light rays are also dispersed.

Description

United States Patent Elbe [451 May 30, 1972 [5 CUT ORNAMENTAL GEM 3,490,250 H1970 712,155 10/1902 [72] Inventor: Maximo Elbe, Hamburg, Germany 93 0 4 2/1992 [73] Assignee: Colorant Schmuckstein GmbH, 2340659 2/1944 H k h 'd B k H b at s 6 an m urg Germany Primary ExammerLou1s G. Mancene [22] Filed: Mar. 31, 1970 Assistant Examiner-D. L. Weinhold [.21] pp NO: 24,225 AttorneyMichaelS. Striker [30] Foreign Application Priority Data [57] ABSTRACT Apr. 1, l969 Germany ..P l9 16 643.9 A di o d i ut to have optically cooperating first facets defining substantially the angle of dispersion so that light rays transmitted through the cooperating facets are dispersed.

[5 l] [5 8] Field of Search ..63/20, 32

[56] References Cited UNITED STATES PATENTS 3,528,261 9/1970 Jones ..63/32 Second optically cooperating facets are also provided which define half the angle of dispersion so that reflected light impinges a facet at the angle of dispersion so that reflected light rays are also dispersed.

15 Claims, 10 Drawing Figures Patented May 30, 1972 5 Sheets-Sheet 1 Inventor: mu" 1 E08? 4,, 0mm I fl Patented May 30, 1972 3,665,729

5 Sheets-Sheet 5 Fig.5

lnvento r [741m 0 F0 8 6- Patented May 30, 1972 I 3,665,729

5 Sheets-Sheet 4 X Inventor: "pum 568! Patented May 30, 1972 3,665,729

5 Sheets-Sheet 5 In vn to r: 174;! M M;

CUT ORNAMENTAL GEM BACKGROUND OF THE INVENTION The present-invention relates to a cut ornamental gem con sisting of a natural or a synthetic refractive material, such as diamond, zirconium, ruby, sapphire or emerald.

Gems of this type do not show any luster in their natural form. Only by cutting and polishing the gem, and providing its surface with facets, a luster and brilliancy is obtained due to the fact that the facets reflect the incident light at the outer and inner surfaces of the stone, and also partly disperse the light into the spectral colors.

A brilliant is made of a diamond by cutting the same in various ways, such as a Parker cut, a Tolkowski cut, or other known cuts. All known cuts cause a substantial loss of incident light, and also a loss of the material of the blank. Furthermore, the coloring or sparkle of the cut gem is only slight. Among other reasons, this is due to the following facts.

In cuts according to the prior art, the table of a brilliant forms angles with rear facets which cause total deflection of perpendicular incident light at the rear facets. The reflected light then emerges at the top portion or bezel at a maximum angle of i6". As a result, the gem appears bright, but shows only few spectral colors because the critical angle of dispersion, for example 23 56' for a diamond, cannot be obtained for the emergent light. Light which impinges obliquely on the table is reflected within the stone and is lost. Therefore, generally speaking, only 33 percent of the incident light is reflected out of the gem. These conditions are due on the one hand, to the constant angle between the table and the rear facets, and on the other hand, to the angle defined between two optically cooperating opposite facets. When a diamond is cut at these angles, up to two-thirds of the materialof the blank diamond or other raw stone is lost. Further losses of light and of rays in the spectral colors occur when the stone is the presence of sparkle and may only be slightly decreased if dispersion of the light into the rays of the spectral colors is desired. The critical angle of dispersion isdifferent for different materials, and is, for example, approximately 23 56' for a diamond. In accordance with the invention, the angle between optically cooperating facets is greater than 16 but less than 23 56', contrary to the position of the facets in conventional brilliants, and is as close as possible to the critical angle of dispersion so that optimum conditions are obtained.

In a preferred embodiment of the invention, the cut gem is a diamond comprising, for the passage of transmitted light rays set with three to eight clamps which not only cover the SUMMARY OF THE INVENTION It is one object of the invention to provide a cut for a gem, particularly for a diamond, which causes light entering the cut gem to emerge in a higher ratio than in gems cut in accordance with the prior art.

Another object of theinvention is to provide a cut for a gem.

by which a very brilliant sparkle is obtained.

Another object of the invention is to cut a gem, and particularly a diamond, in such a manner that a strong coloring is ob- I tained without any significant loss of material.

Another object of the invention is to mount a cut gem in such a manner that the mounting reflects light rays emerging from the cut gem.

Another object of the invention is to mount a cut gem in such a manner that no clamp or other part of the mounting means is located on the top portion of the gem.

Another object of the invention is to cut a gem in such a manner that the total reflection of light within the gem is reduced to a minimum. I

With these objects in view, in accordance with the present invention, the angles between optically cooperating opposite facets of the cut stone correspond for light rays transmitted through the gem to the angle of maximum dispersion of light into rays having the spectral colors. For reflected light rays, the angle between optically cooperating opposite facets corresponds to half the angle of maximum dispersion.

For a particular refractive material used for the cut gem, the divergence from the angle of dispersion is within a range of a few angular degrees, and preferably corresponds to one-sixth of one angular degree.

The teaching of the invention particularly considers the fact that the critical angle of maximum dispersion is decisive for through the gem, optically cooperating opposite facets defining an angle within the range between 16 and 23 56. For reflected light rays, the cut gem comprises optically cooperating opposite facets defining an angle of half the above-stated limits. In comparison with a gem cut in the conventional manner, a particularly lively sparkle is obtained for a gem cut of a diamond if the gem comprises for transmitted light rays, optically cooperating opposite facets defining an angle within the range between 20 and 23 56, and for reflected light rays, optically cooperating opposite facets defining an angle which is between 10 and 11 58'.

In accordance with another feature of the present invention, optically cooperating opposite facets define angles which are greater than the critical angle of dispersion and smaller than the critical angle of reflection of the respective material so that in a diamond cut in accordance with this feature of the present invention, the angles between optically cooperating opposite facets are within a range between 23 56' and 24 30'-. With a cut of this type, only part of the spectral color rays emerge, while another part is totally reflected within the gem so that the gem appears to be luminous with a reddish-yellow color. It is possible to cut only a portion of the gem in the above-explained manner so that not only the color of the gem is improved in comparison with known brilliance, but also a red color effect is obtained.

The sparkle is further enhanced if the bottom surface of the gem is made totally reflecting. For that purpose, the gem may be provided with a coating which is preferably vaporized onto the surface of the gem. Such a coating can be also used for setting the gem by soldering the coating on the bottom portion of the gem to the mounting means. It is advantageous if the gem is embedded in a seat of the mounting material only up to a depth of about one-third of its diameter so that gem projects about two-thirds of its height above the top of the mounting material. 7

The mounting means may also be provided with a reflecting surface preferably on a plate located at the bottom of the gem and having a mirror-reflecting surface on top.

The production of a predetermined spectral color range can be further enhanced, particularly in a diamond, by a further feature of the invention according to which the bottom surface of the gem, and the reflecting surface of the mounting material are spaced from each other a fraction of a predetermined wavelength of the light. In such an arrangement, a red or blue hue of the gem can be obtained, since a part of the light will be extinguished at the bottom of the gem by light reflected by the mounting material.

Furthermore, it has been found that the decorative effect and particularly the sparkle of the gem can be further improved if the usual flat table is transformed into a spherical surface. If the top face of the diamond is cut as a convex spherical face, it will serve as a magnifying lens, making the gem appear larger and capturing the light in an improved manner. The natural shape of the stone blank determines the radius of the spherical surface segment, assuming that as little as possible of the precious material is cut away. The gem may also be provided in accordance with the invention with a similar spherical segment surface on its bottom surface, in

order to gather all the light coming from a light source in a Since an ornamental gem cut in accordance with the invention, can be adapted to the shape of the natural blankstone, a substantial advantage of the invention resides in the extremely small loss of precious material during the cutting operation.

As a result of the several features of the invention, a diamond can be cut to forma gem having interesting color effects, even at an intensity of the impinging light just sufficient for reading purposes.

The novel features which are considered as characteristic for the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a side elevation illustrating a brilliant according to the prior art;

FIG. 2 is a side elevation illustrating a gem cut in accordance with the invention, and a mounting for the same shown in a schematic section;

FIG. 3 is a fragmentary sectional view illustrating a modified arrangement for mounting a gem;

FIG. 4 is a diagrammatic view illustrating the optical conditions for dispersion of light by a facet of a diamond;

FIG. 5 is a plan view illustrating a gem cut in accordance with the invention having sixteen comers and circumferential facets;

FIG. 6 is a schematic vertical sectional view illustrating the dispersion of light reflected in a gem of the invention;

FIG. 7 is a schematic horizontal sectional view of the gem shown in FIG. 6, and illustrating the optical conditions for light transmitted through the gem;

FIG. 8 is a plan view of a gem having afacet ring with nine facets and corners; 2

FIG. 9 is a fragmentary side view illustrating a gem set in accordance with the invention on a reflecting mounting means; and

FIG. 10 is a fragmentary perspective view illustrating the mounted gem shown in FIG. 9.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 illustrates a brilliant according to the prior art in which light rays and 16 impinge perpendicularly on a planar table 11 and are totally'reflected at the facets of the bottom portion 14 so as to emerge again in the form of

light rays

15 and 16 at the table facets or star facets 121. The angle of emergence is smaller than 16 so that the dispersion is only very small. Consequently, perceptible white light emerges only from table 11. Spectral colors can be perceived only on the table or star facets 121 and at the Rondist or corner facets 122, which are substantially covered by the clamps of the setting, not shown. A light ray 17 impinging, for example, at an angle of 45, emerges below the facets as a ray l7 and is consequently lost for the observer. The same is true for the light ray 18 which strikes the main facets of the top portion 12 perpendicularly. This light is lost in the bottom portion at 18'. As a result, under practical conditions and when the gem is mounted, only light striking table 11 perpendicularly is totally reflected at the bottom surface 14 because only in the bottom portion the facets are positioned to obtain total reflection. On the other hand, a great percentage of light entering the brilliant, about two-thirds of the light, is lost. Although the light transmitted through the brilliant without reflection and emerging again at the critical angle of dispersion is split into the rays of the spectral colors, as shown as 17' and 18, it is not visible for the observer and consequently lost.

In contrast, a gem cut in accordance with the invention permits a dispersion into spectral colors due to suitable angles of emergence of light passing directly through the gem, without reflection. Reflected light is also split into spectral colors when emerging from the gem after reflection in the same. For obtaining this result, the optical conditions represented by FIG. 4 have to be considered. FIG. 4 illustrates the refraction of a light ray emerging from the diamond and entering the air. The angle or represents the inclination of the white light ray to the perpendicular on the refractive surface, which is the angle of dispersion and the angle B represents the amount of the splitting of the colored light rays. The larger the difference between the refractive indices is for'the spectral colors red and blue, the more are the. rays of these colors separated, when emerging into air. The refractive indices for red and blue are great for a diamond, and are 2.464 for blue at 0.4;tm, and 2.406 for red light at O.7p.m. The diagram shows the relation between the angle of dispersion o: and the angle 5 at which the light is split.

Since the above-described advantages of the out according to the invention are not fully obtained unless the optical laws regarding the critical angle of dispersion are met, the cut must be carried out under consideration of the diagram. It must he noted, therefore, that light emerging from a dense medium, such as a diamond having n=2.4l into the rare medium,'such as air having rr=l is not only refracted away from the perpendicular on the surface, but also split into spectral colors the more the closer the angle of incidencea approaches the critical angle of dispersion. This critical angle of dispersion is almost 24, for a diamond, with a maximum dispersion of 12 57.

If the angle of incidence is increased beyond the angle of dispersion to the critical angle of reflection of the material, 24 30' for a diamond, the light will be totally reflected within the diamond, and will remain inside the optically denser material.

As can be seen from the diagram in FIG. 4, the critical angle is very important for the spectral color rays of the gem. It is important to maintain the angle of incidence within a range of 30' in relation to the angle of dispersion, in order to obtain optimum results for the splitting of the spectral color rays, which is one of the objects of the invention. In the practice of diamond cutting, this does not represent any particular problems which could cause an increase of the cutting costs over the costs of conventional cuts. As far as the tooling is concerned, there is no difiiculty in cutting the required angles at a tolerance of i 10'. In the present case, and for a diamond, the critical angle of dispersion is in the range between 2330 and 2356, which corresponds to a splitting of the color spectral rays from 8 to 1257.

It is evident that the gem will emit the more colored light, the greater a number of such angles is defined by the facets. Statistically, the incidence of light is dependent upon the actual lighting conditions for any particular position in which the stone is looked at at any particular moment. An excellent splitting of the rays of the spectral colors may already be observed with a decahexagon having angles of 22.5, assuming the light passes directly through the gem. This is due to the fact that the light never strikes a facet in exactly perpendicular direction only. The angle of incidence determines the angle of emergence, so that an angle of emergence of 2356, and therefore also maximum spreading of the spectral color rays can always take place. Nevertheless, substantial differences in the sparkle produced by differently cut gems can be noted. For this reason, it is advantageous to maintain, whenever possible, the above-explained angles between opposite facets. When the gem is provided with facet rings having an even number of facets, this can be realized by positioning optically cooperating opposite facets of two facet rings in offset staggered positions. However, the angles for light reflected in the gem, and light transmitted through the gem, must be different, as will be explained hereinafter, in greater detail.

Referring now to FIG. 2, a gem cut from a spherical diamond has the basic shape shown in FIG. 2. However, if the original shape of the raw diamond, or other stone, is unsymmetrical, it can be cut in a more or less unsymmetrical arrangement of facets in a manner which produces excellent results, and a lively sparkle can be obtained without any major loss of material. Therefore, an unsymmetrically cut gem is not necessarily of a lower quality.

In the finished gem shown in FIG. 2, two adjacent facet rings 24 and 25 each comprise a plurality of facets arranged between the upper spherical segment face 21 which has the shape of a magnifying lens and a height which corresponds to percent of the diameter, and the lower spherical segment face 22 which has a height of about 30 percent of the diameter. The number of the facet rings depends on the shape of the raw diamond and is determined by the critical angle of dispersion of 2356, and by the size of the facet. When using a diamond under consideration of the criticalangle of dispersion, an incident light ray will be totally reflected at the central spherical bottom face 22, then strike facet 25, and emerge as a ray 20 at a spreading angle of 12.

FIG. 3 shows only the bottom portion of a cut diamond which is set into a spherical seat in a mounting material 32, and has an annular recess or groove 31 into which an annular plate 33 projects for holding the gem. Plate 33 is made integral with mounting means 32, for example, by soldering.

In the embodiments of FIGS. 2 and 3, total reflection of incident light at the spherical bottom face may also be obtained by a vaporized mirror-reflecting coating of the surface of the bottom portion, or by a highly polished surface on the seat of the mounting material in which the gem is set. In both cases, the gem will be seated in the mounting means in such a manner that a major portion of the gem is completely exposed to light, as well as to viewing by an observer. In the embodiment of FIG. 2, the setting of the gem may be effected by soldering the gem by its vaporized reflective coating to the mounting material. Due to the total reflection at the bottom part of the gem, it is impossible for light entering the stone to be lost, in contrast to the light losses of conventional brilliants.

The difference regarding the angles of incidents for reflected light and for transmitted light passing through the gem, will now be explained with reference to FIGS. 6 and 7.

FIG. 6 illustrates the condition for light reflected by a facet of the gem, and only then emerging from the same. As shown in FIG. 6, a light ray 62 strikes the table 61 perpendicularly, and is totally reflected by facet 63 of the bottom section. Facet 63 has an inclination to the table face 61 which is 1 158 for a diamond. The reflected light therefore strikes the table 61 at an angle of incidence of 2356, equal to the critical angle of dispersion, and emanates as the dispersed ray 62' at an angle of 1257, so that maximal dispersion is obtained.

FIG. 7 shows in horizontal section the conditions for transversely transmitted light. Light rays 72 pass perpendicularly through the facet 71, and then strike

facets

73 and 74 at the critical angle of dispersion since these facets are cut at an angle of 2356 to facet 71. The light emerging from the gem at

facets

73 and 74, will be split to a maximum angular width of 1257.

Optically cooperating

facets

71,73,74 can be multiplied, and, for example, three systems of three facets can be arranged along a circle 75 as shown in FIG. 8 in which a ring of nine facets is shown. The maximum error which may arise in such an arrangement, amount to about 3 percent which, however, does not have any disturbing influence if irregularities due to the natural shape of the stone are present anyway.

In the embodiment shown in FIG. 8, the three mutually corresponding optical systems are formed by the facet 81 with

facets

82,83, by facet 84 with

facets

85 and 86, and by facet 87 with

facets

88 and 89. In this nonagon, the critical angles of dispersion are always obtained, and cause the dispersion of incident light into dispersed light consisting of spectral color rays. Moreover, light which impinges perpendicularly, for example on facet 85, is dispersed at the maximum angle of dispersion at the intersection of the

facets

84 and 82 so that there is practically no viewing angle, or no position of the gem, in which the gem would not show spectral colors.

In this arrangement, it is necessary that the number of corhers and facets in each facet ring is odd so that the light does not pass through the gem without refraction. The angle of incidence on the facet where transmitted light emerges, must then correspond to a critical angle of dispersion.

Since in a relatively big gem, the facets of a nonagon have a relatively large surface, and since by the cutting operation a great deal of material would have to be removed, it is advantageous to interlace adjacent facet rings in a position in which the respective facets are staggered, and each facet of each facet ring projects between two facets of respective other facet rings.

It must be taken into account that among the angles of incidence, there may also be angles which result in angles of emergence from the gem which are within the angle of total reflection, for example, in a diamond angles greater than 2430 so that the light will be repeatedly or continuously reflected within the gem. This produces a resonance effect which is comparable to the condition producing a laser beam, and due to this efiect, the gem will appear very bright. The effect is indicated by the light rays 51 or 51, respectively, impinging on an angle of 45 in FIG. 5.

FIG. 9 shows a finished gem 91 which is set on a mounting plate 92 provided with a fully reflecting coating. At the rear face of plate 92, a ring 93 is secured for holding the jewel on a finger. Two

light rays

94 and 95 are shown to strike the gem 91 and the reflecting surface of mounting plate 92, respectively. Ray 95 passes through gem 91 and is reflected by the same. Ray 94 directly impinges the reflecting surface of plate 92 and is reflected through the gem 91, increasing the sparkle of the same. As a result, a person looking at the jewel may perceive on the gem a red area 56, and a blue area 97 in the mirror image of the gem 91 on plate 92, as shown in FIG. 10.

It will be understood that each of the elements described above, or two or more together, may also find a useful application in other types of cut gems and jewels differing from the types described above.

While the invention has been illustrated and described as embodied in a gem cut under consideration of the critical angles of dispersion and reflection for increasing the sparkle, it is not intended to be limited to the details shown, since various modifications and structural changes may be made without departing in any way from the spirit of the present invention.

I Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can by applying current knowledge readily adapt it for various applications without omitting features that, from the standpoint of prior art, fairly constitute essential characteristics of the generic or specific aspects of this invention and, therefore, such adaptations should and are intended to be comprehended within the meaning and range of equivalence of the following claims.

What is claimed as new and desired to be protected by Letters Patent is set forth in the appended claims.

Iclaim:

1. A cut ornamental gem consisting of transparent refractive material having a given angle of dispersion and a surface comprising opposite optically cooperating first facets including with each other substantially the angle of dispersion of said material so that first light rays transmitted through the gem and entering the same through one of said first facets are dispersed when passing through the respective other first facet out of the gem, and opposite optically cooperating second facets including with each other substantially half said angle of dispersion so that second light rays entering the gem through one of said second facets are reflected by the respective other second facet and impinge at least one second facet at said angle of dispersion whereby the thus reflected second light rays are dispersed when emerging from the gem; whereby a portion of rays impinging on the gem emerges on and the remaining portion is totally reflected within said gem to thus enhance the color and sparkle thereof.

2. Ornamental gem as defined in claim 1 wherein the angle included between said first facets is between said angle of incidence and an angle which is a few degrees smaller; and wherein the angle included between said second facets is between half said angle of incidence and an angle which is half of said few degrees smaller.

3. Ornamental gem as defined in claim 1 wherein the angles between said first facets deviates within a range of i 10 angular minutes from the angle of dispersion; and wherein the angles between said second facets deviate within a range of i 10 angular minutes from half the angle of dispersion.

4. Ornamental gem as defined in claim 1 wherein the angle between said first facets is greater than the critical angle of incidence of said material and smaller than the critical angle of total reflection.

5. Ornamental gem as defined in claim 1 wherein said material is a diamond; wherein said first facets include an angle between and 23 56'; and wherein said second facets include an angle between 10 and 1 1 58'.

6. Ornamental gem as defined in claim 1 wherein said material is a diamond; wherein said first facets include an angle greater than 16 and smaller than 24 30'; and wherein said second facets include an angle greater than 8 and smaller than 12 15'.

7. Ornamental gem as defined in claim 1 wherein said surface has facets arranged in facet rings about the gem, the facets of each facet ring having an odd number and forming a polygon.

8. Ornamental gem as defined in claim 7, wherein each of said facet rings has nine facets.

9. Ornamental gem as defined in claim 7, wherein facets are located in two adjacent facet rings; wherein the facets of said two facet ringsare staggered and alternate with each other in circumferential direction; and wherein each facet of each facet ring is partly disposed between two facets of the respective other facet ring.

10. Ornamental gem as defined in claim 1 wherein the facets of said opposite facets form facet rings, respectively, about the gem; wherein the number of facets in each facet ring is even; and wherein said facets of said facet rings are staggered.

11. Ornamental gem as defined in claim 1 wherein said surface of said gem includes a spherical convex surface portion located centrally on the top portion of said gem.

l2. Ornamental gem as defined in claim 1 wherein said surface of said gem includes a spherical convex surface portion located centrally on the bottom portion of said gem.

13. Ornamental gem as defined in claim 1 wherein said gem has a main axis; and wherein said surface is cut asymetrically to said main axis in accordance with the shape of a natural stone blank.

14. Ornamental gem consisting of a transparent refractive material and having a surface comprising optically cooperating opposite facets including with each other angles greater than the critical angle of dispersion and smaller than the critical angle of reflection of said refractive material.

15. Ornamental gem as defined in claim 14, wherein said refractive material is a diamond; and wherein said angle between said opposite faces is between 23 56' and 24 30.

Claims

3. Ornamental gem as defined in claim 1 wherein the angles between said first facets deviates within a range of + or - 10 angular minutes from the angle of dispersion; and wherein the angles between said second facets deviate within a range of + or - 10 angular minutes from half the angle of dispersion.

5. Ornamental gem as defined in claim 1 wherein said material is a diamond; wherein said first facets include an angle between 20* and 23* 56''; and wherein said second facets include an angle between 10* and 11* 58''.

6. Ornamental gem as defined in claim 1 wherein said material is a diamond; wherein said first facets include an angle greater than 16* and smaller than 24* 30''; and wherein said second facets include an angle greater than 8* and smaller than 12* 15''.

9. Ornamental gem as defined in claim 7, wherein facets are located in two adjacent facet rings; wherein the facets of said two facet rings are staggered and alternate with each other in circumferential direction; and wherein each facet of each facet ring is partly disposed between two facets of the respective other facet ring.

12. Ornamental gem as defined in claim 1 wherein said surface of said gem includes a spherical convex surface portion located centrally on the bottom portion of said gem.

15. Ornamental gem as defined in claim 14, wherein said refractive material is a diamond; and wherein said angle between said opposite faces is between 23* 56'' and 24* 30''.