Three-dimensional logical puzzles

Abstract

Semiregular or irregular polyhedron-based puzzles have at least two different types of faces. The dividing method used to create the puzzles requires that bisecting planes parallel to the faces be chosen to exclude at least one type of face. Preferably, the base polyhedron has a Buckyball (soccer ball) shape. Applying this dividing method to a Buckyball polyhedron results in (i) a center element with six axes passing through geometrical centers of pentagonal faces, (ii) twelve pentagonal rotating elements, and (iii) thirty mobile elements of tetrahedral shape. The mobile elements are exchangeable between adjacent groups. In another embodiment, sliding elements are superimposed over the mobile elements to enable sliding motion in addition to shifting/rotating motion. Different indicia patterns can be used to modulate the difficulty level of the puzzle. The same dividing method can be used on a sphere to obtain a completely spherical puzzle.

1 . A three-dimensional semiregular or irregular polyhedron-based logical puzzle having at least two different types of outer faces, the puzzle created by a dividing method requiring that bisecting planes parallel to the faces be chosen to exclude at least one type of face, thus defining excluded faces, the puzzle comprising at least three types of elements:
 (a) a center element having at least six non-orthogonal axes passing through the geometrical center of some or all of the outer faces of the polyhedron and passing through the geometrical center of the puzzle, but without passing through the excluded faces;   (b) a plurality of rotating elements rotationally connected to the center element, the rotating elements obtained through the bisecting planes used to slice the base polyhedron on every outside face corresponding to the axes; and   (c) a plurality of mobile elements obtained through the bisecting planes slicing the excluded faces, the mobile elements interfitting with adjacent rotating elements and/or mobile elements to prevent disassembly of the puzzle and to enable one of the rotating elements and an associated plurality of the mobile elements to rotate in a group around its respective axis, whereby rotation of the group enables a user to interchange mobile elements between adjacent groups.   
   
   
       2 . The logical puzzle as claimed in  claim 1  wherein the polyhedron is a Buckyball-shaped polyhedron having six pairs of opposed rotating elements rotationally connected to the center element about six non-orthogonal axes, the Buckyball polyhedron having thirty-two faces including twelve pentagonal faces and twenty hexagonal faces, wherein the puzzle comprises:
 (a) one center element with exactly six axes passing through the geometrical center of the puzzle and through the geometrical center of each opposed pentagonal face;   (b) twelve rotating elements rotationally connected to the center element, the rotating elements obtained through the bisecting planes used to slice the Buckyball-shaped polyhedron, the bisecting planes being parallel to each of the pentagonal faces;   (c) thirty mobile elements obtained through the bisecting planes slicing bisected hexagonal faces, the bisecting planes passing through the geometrical centers of the bisected hexagonal faces, the mobile elements interfitting with adjacent rotating elements to prevent disassembly of the puzzle and to enable one of the rotating elements and five of the mobile elements to rotate as a group around its respective axis, whereby rotation of the group interchanges the mobile element positions.   
   
   
       3 . The logical puzzle as claimed in  claim 2  wherein the center element is an axial rod system having six opposed extensions extending radially outwardly from the center of the polyhedron in alignment with the geometrical centers of each pentagonal face of an invisible regular central dodecahedron, thus providing a total of twelve extensions for rotationally connecting each of the twelve rotating elements to the center element. 
   
   
       4 . The logical puzzle as claimed in  claim 2  wherein the center element is an inner core central element formed by a central regular dodecahedron located at the geometric center of the polyhedron-based puzzle having bores for rotationally connecting each rotating element to the center element. 
   
   
       5 . The logical puzzle as claimed in  claim 4  wherein the inner core center element is formed by snapping together two half dodecahedral elements having protrusions facing inwardly and outwardly for mating the half dodedahedral elements together. 
   
   
       6 . The logical puzzle as claimed in  claim 2  wherein each of the rotating elements is shaped like an angularly extruded pentagon comprising one outward face forming one of the twelve outer pentagonal surfaces of the Buckyball polyhedron, the rotating element further comprising five obliquely angled triangular faces shaped as equilateral triangles, forming part of five of twenty bisected hexagonal faces in the puzzle. 
   
   
       7 . The logical puzzle as claimed in  claim 6  wherein each rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer arranged within concentric bores, one external bore being situated at the geometrical center of the pentagonal face and one internal bore situated in a protrusion, the internal bore serving to position the rotating element on the center element concentric with its respective axis, the bores dimensioned to provide a dividing thickness between the bores to locate the rotating element at an exact distance from the geometrical center of the polyhedron. 
   
   
       8 . The logical puzzle as claimed in  claim 6  wherein each rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer fixed to an internal bore situated at a geometrical center of a protrusion of each rotating element, the protrusion serving to position the rotating element on the center element concentric with its respective axis, and to locate the rotating element at an exact distance from the geometrical center of the polyhedron. 
   
   
       9 . The logical puzzle as claimed in  claim 6  wherein the rotating element comprises a plurality of concealed faces, each concealed face having an arcuate face that cooperates with another arcuate face to define arcuate guiding taper faces enabling sliding movement relative to a mobile element. 
   
   
       10 . The logical puzzle as claimed in  claim 2  wherein the mobile element is generally shaped like opposed quasi-tetrahedrons having two equilateral triangular outer faces and two generally triangular concealed internal faces coplanar with surfaces of the adjacent rotating elements. 
   
   
       11 . The logical puzzle as claimed in  claim 10  wherein the mobile element comprises a tapered protrusion for interfitting the mobile element to adjacent rotating elements, thereby allowing rotation of the mobile elements with one of the adjacent rotating elements as a group around a rotational axis of the rotating element. 
   
   
       12 . The logical puzzle as claimed in  claim 2  wherein the rotating elements and mobile elements further comprise retaining grooves for enabling superimposed sliding elements to slide relative to the rotating elements and mobile elements. 
   
   
       13 . The logical puzzle as claimed in  claim 12  comprising  120  sliding elements that are slidingly superimposed within grooves formed within  30  concealed mobile elements and  12  rotating elements. 
   
   
       14 . The logical puzzle as claimed in  claim 13  wherein the center element is an axial rod system having six opposed extensions extending radially outwardly from the center of the polyhedron in alignment with the geometrical centers of each pentagonal face of an invisible regular central dodecahedron, thus providing a total of twelve extensions for rotationally connecting each of the twelve rotating elements to the center element. 
   
   
       15 . The logical puzzle as claimed in  claim 13  wherein the center element is an inner core central element formed by a central regular dodecahedron located at the geometric center of the polyhedron-based puzzle having bores for rotationally connecting each rotating element to the center element. 
   
   
       16 . The logical puzzle as claimed in  claim 15  wherein the inner core center element is formed by snapping together two half dodecahedral elements having protrusions facing inwardly and outwardly for mating the half dodedahedral elements together. 
   
   
       17 . The logical puzzle as claimed in  claim 13  wherein each of the rotating elements is shaped like an angularly extruded pentagon comprising one outward face forming one of the twelve outer pentagonal surfaces of the Buckyball polyhedron, the rotating element further comprising five obliquely angled triangular faces shaped as equilateral triangles, forming part of five of twenty bisected hexagonal faces of the puzzle, arcuate retaining grooves being formed in every equilateral triangular outer face of the rotating elements for slidingly receiving superimposed sliding elements, the arcuate retaining grooves being concentric with a base vertex of the equilateral triangular outer face, thus guiding the sliding elements in rotation around the base vertex while securing the sliding elements to the puzzle. 
   
   
       18 . The logical puzzle as claimed in  claim 17  wherein each rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer arranged within concentric bores, one external bore being situated at the geometrical center of the pentagonal face and one internal bore situated in a protrusion, the internal bore serving to position the rotating element on the center element concentric with its respective axis, the bores dimensioned to provide a dividing thickness between the bores to locate the rotating element at an exact distance from the geometrical center of the polyhedron. 
   
   
       19 . The logical puzzle as claimed in  claim 17  wherein each rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer fixed to an internal bore situated at a geometrical center of a protrusion of each rotating element, the protrusion serving to position the rotating element on the center element concentric with its respective axis, and to locate the rotating element at an exact distance from the geometrical center of the polyhedron. 
   
   
       20 . The logical puzzle as claimed in  claim 17  wherein the rotating element comprises a plurality of concealed faces, each concealed face having an arcuate face that cooperates with another arcuate face to define arcuate guiding taper faces enabling sliding movement relative to a concealed mobile element. 
   
   
       21 . The logical puzzle as claimed in  claim 13  wherein each concealed mobile element comprises opposed quasi-tetrahedrons having two equilateral triangular concealed outer faces and two generally triangular concealed internal faces coplanar with surfaces of the adjacent rotating elements, the triangular concealed outer faces having arcuate semi-circular retaining grooves for sliding of the sliding elements concentrically with a base vertex of the equilateral triangular concealed outer face, thus guiding the sliding elements in rotation around the base vertex while securing the sliding elements to the puzzle. 
   
   
       22 . The logical puzzle as claimed in  claim 21  wherein the concealed mobile element comprises a tapered protrusion for interfitting the concealed mobile element to adjacent rotating elements, thereby allowing rotation of the mobile elements with one of the adjacent rotating elements as a group around a rotational axis of the rotating element. 
   
   
       23 . The logical puzzle as claimed in  claim 13  wherein the concealed mobile elements and the rotating elements comprise arcuate retaining grooves for slidingly receiving superimposed sliding elements shaped as equilateral triangles arranged in clusters of six triangular sliding elements superimposed over each hexagonal face of the puzzle. 
   
   
       24 . The logical puzzle as claimed in  claim 23  wherein the sliding element comprises a protrusion at its base acting as a guiding tongue to engage the sliding elements in respective arcuate retaining grooves of the concealed mobile elements and of the rotating elements, the arcuate retaining grooves of the elements constituting one of the hexagonal faces together forming a circular slideway to slideably connect each sliding element for rotation as a cluster of six sliding elements, each circular slideway being concentric with a respective center vertex of the respective hexagonal face. 
   
   
       25 . A spherical puzzle created by cutting a plurality of outer spherical sections from a sphere using cutting planes parallel to each of the faces of a guiding regular polyhedron having at least twelve faces, the puzzle comprising:
 i) a plurality of rotating elements having a convex outer face defining a portion of a sphere;   ii) a plurality of first mobile elements connected to each of the rotating elements;   iii) a plurality of second gap elements connected to each of the rotating elements between each of the first mobile elements;   whereby the rotating elements, the first mobile elements and the second gap elements together constitute a complete sphere and wherein the rotating elements and their respective groups of first and second elements together define overlapping circles on the sphere to enable interchanging of first and second elements of one group with first and second elements of another adjacent group.   
   
   
       26 . The spherical puzzle as claimed in  claim 25  further comprising a center element defining at least  6  axes, wherein the rotating elements are rotationally connected to the center element. 
   
   
       27 . The spherical puzzle as claimed in  claim 26  wherein the guiding regular polyhedron is a dodecahedron, thus cutting the sphere into twelve outer spherical sections that partially overlap, the spherical puzzle thus comprising  12  spherical rotating elements rotationally connected in opposed pairs to the center element about  6  axes, wherein the first mobile elements comprise  30  spherical mobile elements adjacent to the spherical rotating elements, and wherein the second gap elements comprise  20  spherical gap elements. 
   
   
       28 . The logical puzzle as claimed in  claim 27  wherein the center element is an axial rod system having six opposed extensions extending radially outwardly from the center of the polyhedron in alignment with the geometrical centers of each pentagonal face of an invisible regular central dodecahedron, thus providing a total of twelve extensions for rotationally connecting each of the twelve rotating elements to the center element. 
   
   
       29 . The logical puzzle as claimed in  claim 27  wherein the center element is an inner core central element formed by a central regular dodecahedron located at the geometric center of the polyhedron-based puzzle having bores for rotationally connecting each rotating element to the center element. 
   
   
       30 . The logical puzzle as claimed in  claim 29  wherein the inner core center element is formed by snapping together two half dodecahedral elements having protrusions facing inwardly and outwardly for mating the half dodedahedral elements together. 
   
   
       31 . The spherical puzzle as claimed in  claim 27  wherein each of the twelve outer spherical sections comprise a spherical rotating element rotationally connected to a center element and a group of spherical mobile elements connected to the spherical rotating element for rotation in unison with the spherical rotating element, wherein each spherical rotating element is a convexly curved pentagon. 
   
   
       32 . The spherical puzzle as claimed in  claim 31  wherein each spherical rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer arranged within concentric bores, one external bore being situated at the geometrical center of the convexly curved pentagonal face and one internal bore situated in a protrusion, the internal bore serving to position the spherical rotating element on the center element concentric with its respective axis, the bores dimensioned to provide a dividing thickness between the bores to locate the spherical rotating element at an exact distance from the geometrical center of the spherical puzzle. 
   
   
       33 . The spherical puzzle as claimed in  claim 31  wherein each spherical rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer fixed to an internal bore situated at a geometrical center of a protrusion of each spherical rotating element, the protrusion serving to position the spherical rotating element on the center element concentric with its respective axis, and to locate the spherical rotating element at an exact distance from the geometrical center of the spherical puzzle. 
   
   
       34 . The spherical puzzle as claimed in  claim 31  wherein the spherical rotating element comprises a plurality of concealed faces, each concealed face having an arcuate face that cooperates with another arcuate face to define arcuate guiding taper faces for interfitting spherical mobile elements and spherical gap elements. 
   
   
       35 . The spherical puzzle as claimed in  claim 27  wherein the spherical mobile elements comprise five convexly shaped generally oblong elements having outwardly curved sides whereas the second gap elements comprise five generally spherical triangular elements that occupy the generally triangular gaps between adjacent oblong elements. 
   
   
       36 . The spherical puzzle as claimed in  claim 35  wherein each spherical mobile element and each spherical gap element comprises a tapered protrusion for rotational interfitting with adjacent spherical rotating elements, mobile elements and spherical gap elements. 
   
   
       37 . The spherical puzzle as claimed in  claim 27  comprising one center element with exactly  6  axes;  12  modified spherical rotating elements modified to have grooves therein; 30 modified spherical mobile elements modified to have grooves therein; 20 modified concealed spherical gap elements modified to rotationally support 20 spherical-gap cap elements; and 60 spherical rotating cap elements and 60 spherical mobile cap elements having protrusions for engaging the grooves for superimposed sliding relative to the modified spherical rotating elements, modified spherical mobile elements and modified concealed spherical gap elements. 
   
   
       38 . The spherical puzzle as claimed in  claim 37  wherein the center element is an axial rod system having six opposed extensions extending radially outwardly from the center of the spherical puzzle in alignment with the geometrical centers of each pentagonal face of an invisible regular central dodecahedron, thus providing a total of twelve extensions for rotationally connecting each of the twelve modified spherical rotating elements to the center element. 
   
   
       39 . The spherical puzzle as claimed in  claim 37  wherein the center element is an inner core central element formed by a central regular dodecahedron located at the geometric center of the spherical puzzle having bores for rotationally connecting each modified spherical rotating element to the center element. 
   
   
       40 . The spherical puzzle as claimed in  claim 39  wherein the inner core center element is formed by snapping together two half dodecahedral elements having protrusions facing inwardly and outwardly for mating the half dodedahedral elements together. 
   
   
       41 . The spherical puzzle as claimed in  claim 37  wherein the modified spherical rotating elements are convexly-shaped, generally pentagonal elements comprising arcuate retaining grooves for receiving superimposed spherical sliding elements that slide in the grooves with respect to the modified spherical rotating elements, the arcuate retaining grooves in the convexly-shaped outer faces being concentric with base vertices of the convexly-shaped generally pentagonal outer face, thus guiding the sliding elements in rotation around the base vertices while securing the sliding elements to the puzzle. 
   
   
       42 . The spherical puzzle as claimed in  claim 41  wherein each modified spherical rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer arranged within concentric bores, one external bore being situated at the geometrical center of the pentagonal face and one internal bore situated in a protrusion, the internal bore serving to position the modified spherical rotating element on the center element concentric with its respective axis, the bores dimensioned to provide a dividing thickness between the bores to locate the modified spherical rotating element at an exact distance from the geometrical center of the spherical puzzle. 
   
   
       43 . The spherical puzzle as claimed in  claim 41  wherein each modified spherical rotating element comprises a rotational mechanism having a screw, a coil spring, and at least one washer fixed to an internal bore situated at a geometrical center of a protrusion of each modified spherical rotating element, the protrusion serving to position the modified spherical rotating element on the center element concentric with its respective axis, and to locate the modified spherical rotating element at an exact distance from the geometrical center of the spherical puzzle. 
   
   
       44 . The spherical puzzle as claimed in  claim 41  wherein the modified spherical rotating element comprises a plurality of concealed faces, each concealed face having an arcuate face that cooperates with another arcuate face to define arcuate guiding taper faces enabling interfitting with, and sliding movement relative to, the modified spherical mobile elements and modified concealed spherical gap elements. 
   
   
       45 . The spherical puzzle as claimed in  claim 37  wherein the modified spherical mobile elements are convexly-shaped generally oblong elements having outwardly curved sides comprising arcuate retaining groove for receiving superimposed spherical sliding elements that slide in the grooves with respect to the modified spherical mobile elements. 
   
   
       46 . The spherical puzzle as claimed in  claim 45  wherein each modified spherical mobile element comprises a tapered protrusion for slidingly interfitting the modified spherical mobile element with adjacent elements. 
   
   
       47 . The spherical puzzle as claimed in  claim 37  wherein each modified concealed spherical gap element is convexly-shaped generally triangular, and wherein each modified concealed spherical gap element rotationally supports a superimposed spherical gap-cap element about which a cluster of superimposed spherical sliding elements may be rotated. 
   
   
       48 . The spherical puzzle as claimed in  claim 47  wherein each modified concealed spherical gap element comprises a tapered protrusion for slidingly interfitting the modified concealed spherical gap element with adjacent elements. 
   
   
       49 . The spherical puzzle as claimed in  claim 37  wherein each spherical gap-cap element is convexly-shaped generally triangular. 
   
   
       50 . The spherical puzzle as claimed in  claim 49  wherein each spherical gap-cap element comprises a tapered protrusion for being rotationally mounted to a respective underlying modified concealed spherical gap element. 
   
   
       51 . The spherical puzzle as claimed in  claim 37  wherein each spherical rotating cap element is convexly-shaped generally triangular having one curved side defining a circular arc. 
   
   
       52 . The spherical puzzle as claimed in  claim 51  wherein each spherical rotating cap element comprises a tapered protrusion for sliding engagement within a circular slideway defined by the grooves of underlying elements. 
   
   
       53 . The spherical puzzle as claimed in  claim 37  wherein each spherical mobile cap element is convexly-shaped generally oblong having one curved side defining a circular arc. 
   
   
       54 . The spherical puzzle as claimed in  claim 53  wherein each spherical mobile cap element comprises a tapered protrusion for sliding engagement within a circular slideway defined by the grooves of underlying elements. 
   
   
       55 . The logical puzzle as claimed in  claim 12  comprising a visual indicia pattern displayed on the outer surface of the elements of the puzzle wherein the pattern has seven indicia locations L 1 -L 7  situated on exposed faces of the puzzle representing seven different visual indicia S 1 -S 7  and wherein the indicia pattern for the puzzle is generated based on a layout shaped like a six-pointed inner hexagon star formed by one inner hexagonal face, three uniformly distributed pentagonal star points being part of three adjacent pentagonal faces and three uniformly distributed hexagonal star points being part of adjacent hexagonal faces, each trapezoidal side face of the sliding elements situated at the circumferential boundary of the inner hexagonal face being assigned a boundary indicia location symbol number from L 2  to L 7  starting with L 2  being assigned to a first trapezoidal side face located at the circumferential boundary of the inner hexagonal face and one of the three adjacent pentagonal faces, the remaining trapezoidal side faces being assigned boundary indicia location symbol numbers from L 3  to L 7 , every other face included in the inner hexagonal faces being identified by an inner indicia location symbol number L 1 , the indicia pattern being further generated by adding cross references identified by the boundary indicia location symbol number L 1  for all three of the pentagonal star points at locations closest to the circumferential boundary of the inner hexagonal face and three other L 1  references on all trapezoidal side faces of the sliding elements contiguous with the circumferential boundary of the inner hexagonal face and situated on all three of the adjacent hexagonal faces, the indicia pattern being completed by repeating every boundary indicia location symbol number from L 2  to L 7  at the tip of every respective pentagonal and hexagonal star points, the indicia pattern being repeated for all or a subset of the twenty hexagonal faces of the puzzle using all or a subset of the seven indicia location symbol numbers L 1  to L 7  representing all or a subset of the thirty-two visual indicia S 1  to S 32  to be displayed on the puzzle. 
   
   
       56 . The logical puzzle as claimed in  claim 55  comprising a visual indicia pattern wherein each cluster of six triangular elements on each hexagonal face has a specific visual indicium common to each of the six triangular elements. 
   
   
       57 . The logical puzzle as claimed in  claim 55  wherein the visual indicia pattern further comprises visual indicia displayed on the pentagonal faces, thereby challenging a user of the puzzle to attempt to position the reassembled cluster adjacent a side of the pentagonal face having the visual indicium corresponding to the visual indicium displayed on the elements of the cluster. 
   
   
       58 . The logical puzzle as claimed in  claim 55  wherein the visual indicia pattern comprises one of up to twenty different visual indicia S 1  to S 20  for each cluster of six sliding elements associated with each of the twenty hexagonal faces of the puzzle, and further comprises twelve additional visual indicia S 21  to S 32  for identifying the pentagonal faces of the Buckyball polyhedron.