WO1983003773A1

WO1983003773A1 - A decahedral die or game piece

Info

Publication number: WO1983003773A1
Application number: PCT/DK1983/000048
Authority: WO
Inventors: Jo^/rgen Nikolaj JUHLDAL; Gunnar Olof Sundien
Original assignee: Individual
Current assignee: Individual
Priority date: 1982-04-26
Filing date: 1983-04-25
Publication date: 1983-11-10
Anticipated expiration: 1984-10-26
Also published as: DK184082A; GB8334114D0; GB2129694A

Abstract

A die or game piece consists of ten mutually congruent, differently marked quadrangular faces, forming two identically shaped five-sided opposite placed pyramids with a common axis, the two pyramids being turned around the axis over an angle of 36?o to each other. Each of the side faces of one of the pyramids is parallel to one side face on the other pyramid. Each quadrangular side face has two opposite angles of 90?o, while the two other opposite angles are about 52?o and 128?o, respectively. The die is, when the ten side faces are marked in succession from 0 to 9, suitable as a random number generator, producing a single cipher. Several throws with one die or a single throw with several dice can generate a random number having a corresponding number of ciphers.

Description

A decahedral die or game piece

The present invention relates to a die or game piece ha¬ ving ten side faces and formed as indicated in the pre¬ amble of claim 1. Dice of this type are suitable for many different games or for generating random numbers 5 from 0 to 9.

The usual six-sided die will, when throwed randomly, become at rest on any arbitrary side face and thus ge¬ nerate a random number from 1 to 6.

From USP No.: 4239 226 is known a ten-sided die which 10 is composed of two opposite placed pyramids having a common center axis and a common base, the two pyramids being turned 36° in relation to one another around the axis. The surface of this die contiguous the equatorial plane is formed by a convex surface of revolution of an 15 arc having a smaller radius than the distance from the center of the die symmetrically with respect to the plane, about the axis.

In the description of the above mentioned US patent is stated that the invention overcomes the disadvantages 20 of earlier known ten-sided dice as random number genera¬ tors of invariably tumbling from one side to another, wich can lead, wittingly or unwittingly to repetition

-^•* in successive throws.

The object of the random number generator of the above 25 . mentioned US patent is that, because of the circular section, the .die will normally not tumble but rather roll on the convex equatorial surface of revolution and thus rotate around the center axis of the pyramids un¬ til the die is brought to rest on one arbitrary side .30 face.

OMPI In order to obtain a true arbitrary distribution it is necessary, however, that the center axis of the pyramids is kept exactly horizontal when the die is thrown. This precondition is seldom fulfilled in practice. If one and the same person makes a great number of thows the center axis of the pyramids will, inevitably, be held more or less obliquely in relation to the horizontal plane. For this reason, the probability that a side face from one of the pyramids is placed upwards may be diffe- rent from the probability that a side face from the other pyramid is placed upwards.

The present invention is based on another idea, viz. that a uniform and random distribution can be obtained ^' if the die is so formed that all corners of the pyramids, partly the ten corners placed in the equatorial zone and partly the two pyramidal vertices, are placed on the same spherical surface having its center situated on the com¬ mon^" center axis of the pyramids. Such a piece may be thrown like a normal six-sided die and it will be a mat- ter of chance which one of the twelve corners will first hit the supporting plane so that the probability for any of the side faces to be placed upwards will be the same.

This theory has been confirmed by experiments comprising several thousands of throws in which a statistical uniform and random distribution of the result for each side face is obtained.

It can be shown, by calculation, that the precondition for all twelve corners to be placed on the same spherical sur¬ face is that all ten side faces of the pyramids form con- gruent quadrangles in which two opposite angles are rect¬ angular, the two other opposite angles being about 51?8 and 128,2, respectively. In such a die, any of the side faces of one pyramid is placed at right angle to two other side faces of the same pyramid and two side faces of the other pyramid. The piece will then have a har onical and compact form. The die or game piece of the invention has ten side faces, each of which is placed on one of two opposite situated identical five-sided pyramids having a common axis, the two pyramids being turned 36° in relation to one another around the axis, and the die has the ten side faces which are contiguous congruent quadrangles in which two opposite angles are rectangular and the other two opposite angles are about 51 - 8 and 128, 2, respectively, so that all corners of the ten quadrang- les are situated on one and the same spherical surface.

In order to distinguish betwen the ten side faces, dif¬ ferent markings can be used. Thus, the side faces can have different colours. They can also be numbered in succession, for example from 1 to 10 or from 0 to 9, each face can have a different number of dots or other marking. Preferably the faces can have 0 - 9 dots or spots. A marking of this sort is suitable for genera¬ ting a random number or cipher. If the piece is thrown repeatedly a number having a corresponding number of ciphers is generated. The same result is obtained when throwing several pieces in one throw in which case the number of ciphers corresponds to the number of pieces.

The die in question may be produced from any desired material, such as paper, leather, rubber, plastics, wood, metal or ivory- Preferably is used plastics which is useful for mass production using conventional pressing or injection moulding technique, either in one piece or two halves which are glued together. All cor¬ ners may be rounded so that the die may easily roll. The invention is explained further with reference to the drawing, in which

Fig.l is a side view of a ten-sided die according to the invention, seen in a direction parallel to four of the side faces.

OMPI Fig.2 is a view of the same piece at right angle to one of the faces, and

Fig.3 shows all ten sides of the piece, unfolded and placed in the plane of the paper.

The die shown in fig. 1 and 2 is resting with the side face 6 against a supporting plane and having the face 3 placed upwards parallel to the supporting plane. The section shown in fig. 1 is quadratic, enclosed by the faces 3, 4, 5 and 6. The faces 3, 7, 1, 5 and 9 (the last face is not shown in fig.l) form a first py¬ ramid having a vertex 11. A second, opposite pyramid is formed by the side faces 2., 4, 6, 8 and 10 (the faces 2 and 8are not shown in fig. 1) and has a vertex 12.

When viewing the die in the direction of the arrow &_ in"fig.l is seen the section shown in fig.2. The face 5 is placed at right angle to the faces 3 and 7, belong¬ ing to the same pyramid as the face 5_> viz the pyramid with vertex 1. The face 5 is also placed at right angle to the two faces 2 and 6, belonging to the pyramid having the vertex 12.

Fig. 2 can also be regarded as an image of a die, resting on the face 4 against a horizontal supporting plane and seen at right angle to this plane, so that the face will be parallel to the horizontal plane.

In fig. is shown a preferred marking of the ten faces, one of which is marked with a circle and a dot, while the other nine faces have 1 to 9 dots. If the face 10 is ascribed the value 0, the sum of the number of dots on two opposite faces will be 9. It will be understood that the two pyramids are formed when the edge 13 co¬ incides with the edge 14 and when the edge 15 coincides with the edge 16- The angle betwen the two quadrangular faces 13 and 17, having the vertex 20, is 90°. The oppo¬ site angle, i.e. the angle between the quadrangular faces .18 and 19, is also 90 . The angle having a vertex 21 is

about 128°2, and the angle having the vertex 21 is about

51?8.

The three visible faces in fig. 2 is marked in the same way as in fig. 3; no markings are shown in fig. 1, however

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Claims

C L A I M S

1. Die or game piece, having ten side faces, forming two opposite pyramids of identical shape, the two pyramids being turned 36° around a common axis of the pyramids, c h a r a c t e r i s e d in that the ten side faces constitute mutually adjoining congruent quadrangles, two opposite angles of which each being 90°, while the two other opposite angles being about 51,°8and 128,°2 , respecti vely, so that all corners of the quadrangles are placed on one and the same spherical surface.

2. Die or game piece according to claim 1, c h a r a c t e r i s e d in that the ten side faces are differently marked, preferably having 1 - 10 or 0 - 9 dots or similar markings.

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