DIVIDING METHOD FOR THREE-DIMENSIONAL LOGICAL PUZZLES
A dividing method used to easily divide any given solid into perfectly interfitting parts by using at least one guiding polyhedron to establish an axis system serving as guiding paths for associated geometrical figure contours used to slice said given solid. This axis system is coincident with all or a subset of the geometrical centers of each face of the guiding polyhedron, with midpoints of the edges of the polyhedron, and with the vertices of the polyhedron. The dividing method is based on five different techniques: a selecting technique, a sizing technique, a multi-slicing technique, a multi-pivoting technique, and a multi-guiding technique. This dividing method can create extremely challenging, aesthetic and symmetrical three-dimensional puzzles having shifting and optionally sliding features. This dividing method works with polyhedron-based solids, spherical solids and odd-shaped solids of any kind.
The present invention relates generally to a dividing method useful for simply dividing any given solid into perfectly interfitting parts, or making three-dimensional logical puzzles and, in particular, to puzzles having either a spherical shape or a shape based on a polyhedron.
BACKGROUND OF THE INVENTIONThe prior art of shifting-movement puzzles includes regular, semiregular and irregular polyhedra. There are numerous types of polyhedron-based puzzles known in the art. Most of the prior art polyhedron puzzles are based on the five platonic solids and are of very moderate complexity.
Also known in the art are three-dimensional sliding puzzles. Three-dimensional puzzles combining shifting and sliding features have been proposed by Applicant in U.S. patent application Ser. No. 11/738,673 (Paquette) entitled “Three-Dimensional Logical Puzzles”, which was filed on May 2, 2007.
Also known in the art are ball-shaped or spherical puzzles. Spherical shifting puzzles are very scarce due to the great difficulty of properly dividing a sphere in order to obtain a symmetrical, aesthetical and challenging puzzle.
Spherical puzzles created by dividing a sphere based on a guiding regular polyhedron, i.e. by defining outer spherical sections by dividing the sphere parallel to a guiding polyhedron to create overlapping spherical sections on the sphere, are proposed by Applicant in U.S. patent application Ser. No. 11/738,673, supra. A spherical puzzle created by this technique is challenging, entertaining and aesthetically pleasing.
Odd-shaped puzzles, such as a human head for example, are proposed but are of a low difficulty level again due to the complexity of the shape division involved.
Therefore, complexly subdivided regular, semiregular or irregular polyhedron-based puzzles, or spherical puzzles, or odd-shaped puzzles enabling shifting (and optionally also sliding movement) would provide a highly challenging, entertaining and aesthetically-pleasing three-dimensional puzzle.
SUMMARY OF THE INVENTIONAn object of the present invention is to provide an easy, straightforward dividing method useful for making symmetrical, challenging, entertaining and aesthetically pleasing polyhedron-based, or spherical-based, or odd-shape-based puzzles having elements that can be shifted and which can optionally further include superimposed sliding features.
The present disclosure explains a method of dividing any given solid in perfectly interfitting parts by using an axis system associated with a guiding polyhedron. The axes are defined as passing through all or a subset of the geometrical centers of every face, edge midpoints and vertices. Each axis serves as a path along which a planar (two-dimensional) geometrical figure can be projected into an intersecting relationship with the given solid to thereby slice the given solid into perfectly interfitting parts according to the particular contours of the geometrical figure. In other words, a plurality of potentially different geometrical figures, each defining a cutting plane having its own geometrical contours, is used to cuts, or slice, the solid into puzzle elements by intersecting the solid with the various geometrical figures whose respective orientations remain fixed relative to their respective axes.
By properly choosing a suitable guiding polyhedron, axis system and associated geometrical figures, an infinity of aesthetic and challenging three-dimensional puzzles can be produced from various solids.
The exposed dividing method works with polyhedron solids, spheres and odd-shaped solids of any kind. Any polyhedron can be selected as the guiding polyhedron, but the preferred ones for symmetrical reasons are of the convex uniform kind, such as the platonic solids, the archimedean solids and the prism and antiprism solids.
The dividing method exposed in the present disclosure can be easily extended by using superposed polyhedra for guiding purposes, all of which lies within the scope of the present invention.
The embodiments of the present invention will now be described with reference to the appended drawings in which:
These drawings are not necessarily to scale, and therefore component proportions should not be inferred therefrom.
DESCRIPTION OF THE PREFERRED EMBODIMENTSBy way of introduction, the dividing method will be illustrated with simple preferred embodiments related to a regular guiding polyhedron. It is to be understood that any polyhedron or combination of polyhedra can be used as the guiding polyhedron associated with said axis system, all within the scope of the present invention.
The dividing method presented in this disclosure consists of a combination of techniques, a selecting technique, a sizing technique, a multi-slicing technique, a multi-pivoting technique, and a mutli-guiding technique used to create symmetrical, aesthetic and challenging puzzles, or simply used to divide any given solid into perfectly interfitting parts. Of the five techniques presented herein only the two first are essential to the dividing method. The three remaining techniques are optionally used to enhance the puzzle's complexity in order to achieve a greater challenge.
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As mentioned the first technique involved in the dividing method is the selecting technique. This technique refers mainly to the selection of the proper form of every geometrical figure associated with an appropriate axis system to be used for slicing the given solid. The second technique involved in the dividing method is the sizing technique. This technique refers to the selection of the proper dimension, or size, of every associated geometrical figure. Proper selection of the geometrical figures and proper sizing of these figures are essential to the dividing method and depend on the expected purposes of the divided solid. As a general rule for puzzle purposes, very symmetrical parts are sought and as many as possible parts should be interchangeable (shifting-wise). So mostly circular figures are used for puzzle purposes with quite a bit of overlapping of the geometrical figures.
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The mobile elements 22 are grouped around each of the rotating elements 21 in shifting sections whereby mobile elements of one group can be interchanged with mobile elements of other groups. Thus, a shifting spherical puzzle is created by dissecting a sphere with cutting circular geometrical figures that are associated with each face axis f-f of a guiding tetrahedron T to generate overlapping outer spherical sections, each centered about a respective rotating element 21.
Necessary adjustments to convert the given solid elements into a functioning puzzle are well described in the prior art and need no further explanation other than mentioning that:
(i) each rotating element is connected to the puzzle by a retaining means, i.e. a fastener, fastener subassembly, retainer or other retaining mechanisms. These retaining means hold the pieces in an interfitting relationship and enable rotational movement around the associated axis. These retaining means could include a coil spring to reduce friction generated between adjoining surfaces and provide easily movable elements that are not prone to jamming, catching or getting “hung up”. These interconnecting means could be replaced by snapping-action parts, which would also fall within the scope of the present invention;
(ii) holding means are provided for holding the remaining elements in an interfitting relationship with each respective rotating element, or adjacent remaining elements. Usually, the angles formed in the divided parts are such that remaining elements cannot slide out of their fitted position, thus preventing disassembly of the puzzle. Other interfittings, mechanisms or locking means are possible that enable elements to be interchanged from one group or subgroup to another group or subgroup by “shifting” (i.e. twisting or rotating) one group or subgroup relative to the other groups or subgroups. For example, locking means could include a tongue and groove mechanism. It is understood that this groove could be male (protrusion) or female (cavity), and of many shapes like dovetail-shaped, L-shaped or T-shaped or of any shape that provides a retaining means allowing rotation about an axis, all within the scope of the present invention;
(iii) the obtained puzzle can be designed with or without a center element or core located inside of the given solid puzzle, which can be either (a) an inner sphere, or (b) an internal concentric polyhedron, or (c) an axial rod (pivot) system. Depending on the guiding polyhedron used and the selected dividing geometrical figures, the center element may or may not have exposed faces. A coreless puzzle can be constructed by providing the rotating elements, mobile elements, gap elements, and the remaining elements, if applicable, with appropriate protrusions and grooves. These protrusions and grooves cooperate as interfitting male and female connections to slideably and rotatably interlock the various elements to thus hold the elements together to form a complete solid puzzle. Also, the center element could be constructed by the interfitting or snapping action of two half center core elements. When assembled together these two half center core elements form a hollow center core element shaped as a polyhedron or a sphere. With this hollow center core element, the rotating elements are rotationally connected to the core element by a screw inserted from inside the puzzle and thus no capping of elements is required in order to obtain an even and smooth outer surface over the given solid outer shell of the puzzle. All of the previously mentioned possibilities or modifications lie within the scope of the present invention.
The foregoing adjustments (or other similar adjustments well within the capabilities of a person of ordinary skill in the art) are needed to convert the given solid elements in the puzzles presented in the remaining figures of this disclosure so as to obtain functioning (shiftable) puzzles. These modifications and adjustemnts are well within the reach of a person familiar with the art of three-dimensional puzzles and therefore require no further elaboration.
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The last technique of the dividing method, the “multi-guiding technique”, relates to the use of multiple guiding polyhedra used to divide one given solid. This technique corresponds to the superposition of different divisions from different puzzles into only one puzzle. The results of such superposition becomes rapidly complex and for the sake of simplicity only puzzles based on single guiding polyhedra are presented in this disclosure. However, it will be obvious to a person familiar with the art of three-dimensional puzzles, that this technique alone is an extremely powerful tool to create astonishingly complex and intriguing puzzles aimed at the expert enthusiast. But as mentioned in the prior art, with proper indicia pattern selection, the puzzle difficulty level can be modulated to obtain a reasonably solvable puzzle.
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It is to be understood that the same techniques for arranging the display of colours, emblems, logos or other visual indicia on the outer surfaces of the puzzles to modulate the difficulty level of the puzzles presented in the prior art are also applicable to any of the puzzles obtained through the application of the dividing method disclosed herein. Complex descriptions of evoluted patterns are not included in the present disclosure for the sake of simplicity, but are well within the scope of the technology introduced here and can be easily derived from the principles already disclosed in the prior art and applied to the puzzles resulting from the present dividing method. Different visual indicia patterns (e.g. colours, logos, emblems, symbols, etc.) can be used to modulate the difficulty level of the puzzles. In other words, different versions of a given puzzle can be provided for novice, intermediate or expert players, or even for kids.
It should be noted that advertising, corporate logos or team logos could also be placed onto the surfaces of the puzzles obtained by the application of the present dividing method to create promotional vehicles or souvenirs.
Also worth mentioning is that it is possible to add sliding movements to the pre-existing shifting movement to further complicate the puzzles. Slidable elements can be added to underlying shiftable elements as described Applicant's U.S. patent application Ser. No. 11/738,673. Generally, this is done by superimposing permutable sliding elements at the outer face of a given puzzle that slide in grooves in the underlying faces of said given puzzle to provide both shifting and sliding movements. Each superimposed sliding element slides in a curved track (the adjoining grooves) over the outer faces of non-sliding given puzzle elements along a circular slideway groove formed by adjacent grooves. Thus, adding sliding elements to a given shifting puzzle greatly increases the complexity of said given puzzle. Such given puzzle is now said to combine both shifting and sliding features.
All the aforesaid sliding modifications are analogous to the modifications introduced in Applicant's U.S. patent application Ser. No. 11/738,673, and therefore need not be repeated herein.
Other polyhedra of any kind could also be used as the guiding polyhedron for bisecting any given solid with the present dividing method, all without departing from the scope of the present invention. Likewise, the dividing method could also be applied to any polyhedron to achieve and create other interesting and challenging puzzles. Accordingly, the drawings and description are to be regarded as being illustrative, not as restrictive.
It will be noted that exact dimensions are not provided in the present description since these puzzles can be constructed in a variety of sizes.
While the puzzle elements and parts are preferably manufactured from plastic, these puzzles can also be made of wood, metal, or a combination of the aforementioned materials. These elements and parts may be solid or hollow. The motion of the puzzle mechanism can be enhanced by employing springs, bearings, semi-spherical surface knobs, grooves, indentations and recesses, as is well known in the art and are already well described in the prior art of shifting and sliding puzzles. Likewise, “stabilizing” parts can also be inserted in the mechanism to bias the moving elements to the “rest positions”, as is also well known in the art.
It is understood that the above description of the preferred embodiments is not intended to limit the scope of the present invention, which is defined solely by the appended claims.
Claims
1. A method of dividing any given solid into perfectly interfitting parts covering an entire outer surface of a shiftable three-dimensional puzzle, the method comprising steps of:
- selecting at least one guiding polyhedron;
- defining an axis system based on the at least one guiding polyhedron, wherein axes of the axis system passthrough all or a subset of geometrical centers of the faces, edges and vertices of the guiding polyhedron;
- associating, with each axis, a planar geometrical figure contour which can be projected along each respective axis into an intersection with the given solid to be divided; and
- dividing the given solid using the geometrical figure contour into perfectly interfitting parts covering the entire outer surface of the puzzle.
2. The dividing method as claimed in claim 1 wherein the step of associating the geometrical figure contour with each axis comprises steps of selecting a proper form for each geometrical figure contour associated with the axes of the axis system and sizing each geometrical figure contour for dividing the given solid.
3. The dividing method as claimed in claim 2 further comprising a step of applying a multi-slicing technique wherein said given solid is sliced more than once along one or more of the axes of the axis system with geometrical figure contours of a different size.
4. The dividing method as claimed in claim 2 further comprising a step of applying a multi-pivoting technique wherein a circular geometrical figure contour is added to one or more axes of the axis system to divide said given solid into pivoting groups of one or more elements.
5. The dividing method as claimed in claim 2 further comprising a step of applying a multi-guiding technique wherein one or more guiding polyhedra are superimposed as guides for multiple axis systems, with axes passing through all or a subset of geometrical centers of faces, edges and vertices of the guiding polyhedral whereby each axis of every additional axis system is associated with a geometrical figure contour which can be projected into an intersecting relationship with the solid in order to slice the given solid into perfectly interfitting parts covering the entire outer surface of the solid.
6. The dividing method as claimed in claim 1 comprising at least one of the steps of:
- selecting a proper form for each geometrical figure contour associated with axes of the axis system;
- sizing each geometrical figure contour to be used for slicing the given solid;
- applying a a multi-slicing technique wherein the given solid is sliced more than once along at least one axis of the axis system with a geometrical figure contour of a different size;
- applying a multi-pivoting technique wherein a circular geometrical figure contour is added to at least one axis of the axis system to divide said given solid into pivoting group of one or more elements; and
- applying a multi-guiding technique wherein one or more guiding polyhedra are superimposed as guides for axis systems, with axes passing through all or a subset of geometrical centers of faces, edges and vertices of the guiding polyhedra, whereby each axis of each additional axis system is associated with a geometrical figure contour along which the geometrical figure contour can be projected into an intersecting relationship with the solid in order to slice the given solid into perfectly interfitting parts covering the entire outer surface of the solid.
7. The dividing method as claimed in claim 6 wherein the guiding polyhedra are convex uniform polyhedra selected from the five platonic solids, the thirteen archimedean solids, the prism solids, and the antiprism solids.
8. The dividing method as claimed in claim 7 wherein most of the associated geometrical figure contours are circular in order to create a mostly symmetrical three-dimensional puzzle when said given solid is divided, wherein some of the interfitting parts act as pivoting elements while enabling substantially all of the other parts of the puzzle to be shifted.
9. The dividing method as claimed in claim 8 wherein said given solid is a polyhedron.
10. The dividing method as claimed in claim 9 comprising a further step of superimposing sliding elements onto one or more outer surfaces of said puzzle.
11. The dividing method as claimed in claim 8 wherein said given solid is a sphere.
12. The dividing method as claimed in claim 11 comprising a further step of superimposing sliding elements onto one or more outer surfaces of said puzzle.
13. The dividing method as claimed in claim 8 wherein said given solid is an odd-shaped solid.
14. The dividing method as claimed in claim 13 comprising a further step of superimposing sliding elements onto one or more outer surfaces of said puzzle.
Type: Application
Filed: Oct 3, 2007
Publication Date: Apr 9, 2009
Inventor: MAXIME PAQUETTE (Val-Des-Monts)
Application Number: 11/866,713
International Classification: A63F 9/08 (20060101);