Educational device and method

• US 4,650,424 A
• Filed: 07/15/1985
• Issued: 03/17/1987
• Est. Priority Date: 09/30/1982
• Status: Expired due to Fees

• Current Assignee: Maurice E. Mitchell
• Original Assignee: Maurice E. Mitchell
• Inventors: Mitchell, Maurice E.
• Primary Examiner(s): Grieb, William H.
• Application Number:
  US06/754,920
• Time in Patent Office: 610 Days
• Field of Search: 434/211, 434/277, 434/278, 434/281, 434/403, 273/157 R, 446/85, 446/92, 52/DIG. 10
• US Class Current: 434/211
• CPC Class Codes: A63F 2009/1212 magnetic connections
• CPC Class Codes: A63F 2250/606 with suction cups
• CPC Class Codes: A63F 9/12 Three-dimensional jig-saw puzzles
• CPC Class Codes: Y10S 52/10 Polyhedron
• CPC Class Codes: Y10S 52/13 Hook and loop type fastener

Abstract

An educational toy and method for demonstrating characteristics of a latticework of spacepoints including demonstrating (a) the commonality of latticework between tetrahedron configuration latticework and octahedron configuration latticework, (b) that octahedron latticework merges with tetrahedron latticework, (c) the 13-plane structure of the common latticework, (d) how simultaneous twinning in more than one of the 13 planes can form multitudes of combinations of domains of tetrahedrons and octahedrons, and (e) the altering of latticework by appropriately selecting the dimensions of structure members that define spacepoints in the latticework. Preferably, the structure members are similarly dimensioned and oriented ellipsoidal elements which are gravity stacked and optionally connectable and wherein the centerpoint of each ellipsoidal element represents a spacepoint in the latticework. With ellipsoidal elements, the latticework structure is determined by the relative lengths of the three orthogonal axes of symmetry of the ellipsoidal elements when the common axis and the location of either orientation mark are known.

Claims

1. A method of teaching characteristics of latticework structure comprising the steps of:

demonstrating the commonality of lattice structure of (a) latticework arranged in accordance with a tetrahedron configuration and (b) latticework arranged in accordance with a pyramid configuration which has (i) a four-edge base and (ii) four faces that extend from the base and meet at a point, said demonstrating step including the steps of;

positioning a plurality of structural members relative to each other to define spacepoints in a latticework arranged in accordance with the tetrahedron configuration; and

positioning a plurality of structural members relative to each other to define spacepoints in a latticework arranged in accordance with the pyramid configuration;

wherein said positioning steps include;

merging together structural members along at least one face of the latticework arranged in accordance with the tetrahedron configuration with structural members along at least one corresponding face of the latticework arranged in accordance with the pyramid configuration to make the spacepoints along at least one tetrahedron face coexistent with the spacepoints on the at least one corresponding pyramid face.

2. A method according to claim 1 wherein each said positioning step includes the step of:

gravity stacking a plurality of at least substantially similarly dimensioned, similarly oriented ellipsoidal elements wherein each ellipsoidal element is one of the structural members and the centerpoint of each ellipsoidal element is a spacepoint in the latticework;

all stacked ellipsoidal elements having at least substantially similar dimensions.

3. A method according to claim 2 wherein said pyramid configuration stacking step includes the step of:

stacking ellipsoidal elements to form a one-eighth octahedron section that includes one face of a pyramid configuration; and

wherein said merging step includes the step of;

merging the pyramid face of the one-eighth octahedron section with a face of the latticework arranged in accordance with the tetrahedron configuration;

said merging resulting in at least a substantially uniform latticework structure.

4. A method according to claim 3 wherein said demonstrating step includes a further step of:

applying indicia to the ellipsoidal elements;

the indicia being applied and located on the stacked ellipsoidal elements so that the indicia on the ellipsoidal elements display a first identifiable pattern when the latticework is oriented to the first bearing and a second identifiable pattern when the latticework is oriented to a second bearing with a common axis indicia that is oriented in the same bearing in said first bearing and said second bearing.

5. A method according to claim 2 wherein said gravity stacking step includes the step of stacking similarly dimensioned spheroids, the centerpoint of each spheroid being a spacepoint in the latticework.

6. A method according to claim 2 comprising the further step of:

selecting the ellipsoidal element dimensions to have a major axis and two minor axes of prescribed relative lengths that define the latticework structure, the major axis and two minor axes determining the distance between adjacent spacepoints in the latticework.

7. A method as claimed in claim 6 wherein the positioning step includes the step of:

forming the latticework in space of sufficient ellipsoidal elements that the latticework spacepoints define thirteen nonparallel planes in space, each plane being defined by a plurality of coplanar ellipsoidal elements that contact a given ellipsoidal element.

8. A method according to claim 2 wherein said gravity stacking step includes the stacking of magnetically interacting ellipsoids.

9. A method according to claim 2 wherein the positioning step includes the step of:

forming the latticework in space of sufficient ellipsoidal elements that the latticework spacepoints define thirteen nonparallel planes in space, each plane being defined by a plurality of coplanar ellipsoidal elements that contact a given ellipsoidal element.

10. A method according to claim 1 comprising a further step of:

selecting the dimensions of the structural members to determine prescribed distances between each spacepoint in the latticework and spacepoints adjacent to said given spacepoint, the dimensions of the structural members which define inter-spacepoint distances defining the latticework structure, said distances substantially as set forth in Table II Sections (a) through (d), where numbered spacepoints are those in FIG. 7.0 where the common axis is through spacepoints 701 and 702 and the distance between spacepoints 701 and 702 is equal to unit distance `D`.

11. A method for teaching latticework characteristics comprising the step of:

demonstrating the commonality of internal lattice structure between similarly dimensioned, similarly oriented ellipsoidal elements arranged to form (a) a tetrahedron configuration and (b) a pyramid configuration having (i) a base and (ii) four sides, when such configurations are extended in space;

wherein the commonality demonstrating step comprises the steps of;

coupling ellipsoidal elements together to form a cuboctahedral type configuration characterized by having twelve ellipsoidal elements touching one ellipsoidal element;

orienting the ellipsoidal elements in said cuboctahedral type configuration to a first prescribed bearing;

selectively stacking additional ellipsoidal elements relative to the ellipsoidal elements that are coupled and oriented to the first prescribed bearing to form the tetrahedron configuration;

orienting the ellipsoidal elements in said cuboctahedral type configuration to a second prescribed bearing; and

selectively stacking additional ellipsoidal elements relative to the ellipsoidal elements that are coupled and oriented to the second prescribed bearing to form the pyramid configuration having a base and four sides.

12. An educational device for teaching characteristics of latticework structure comprising:

sets of structural members of suitable material, consisting of a plurality of similarly dimensioned tetrahedral structural members and a plurality of similarly dimensioned octahedral structural members;

said structural members having suitable means for connecting congruent faces to each other.

13. An educational device according to claim 12 wherein;

said structural members have suitable markings which indicate the non-twinning orientation of each face of each pair of tetrahedral structural members in relation to the appropriate congruent face of their matching octahedral structural member.

14. An educational device according to claim 13 wherein;

the corner-to-corner distances of said structural members, being essentially equal to the center-to-center distances of spacepoints on said latticework structure where the corner-to-corner distances are substantially equal to the ratios of unit distance `D` as set forth in claim Table II Sections (a) through (d), where numbered spacepoints are those in FIG. 7.0 where the common axis is through spacepoints 701 and 702 and the distance between spacepoints 701 and 702 is substantially equal to unit distance `D`.

15. An educational toy for teaching characteristics of imaginary thirteen nonparallel plane latticework structure comprising:

a plurality of similarly dimensioned ellipsoidal elements, each ellipsoidal element being dimensionally characterized by three orthogonal axes of symmetry and a curved surface in which every plane cross section is an ellipse or a circle, one of said axes being marked as a common axis with a suitable similar indicia on the ellipsoidal surface indicating the correct orientation or bearing of said common axis; and

each ellipsoidal element having a suitable similar indicia on the ellipsoidal surface indicating the correct triangular or tetrahedral orientation of the ellipsoidal element when correctly gravity stacked on a gravity tray, or placed in an imaginary thirteen nonparallel plane latticework structure; and

each ellipsoidal element having a suitable similar indicia on the ellipsoidal surface indicating the correct pyramidal or octahedral orientation of the ellipsoidal element when correctly gravity stacked on a gravity tray, or placed in a imaginary thirteen nonparallel plane latticework structure; and

each ellipsoidal element having six uniquely oriented polarized connecting holes through the centerpoint thereof;

where said six uniquely oriented polarized connecting holes may optionally be connected to an identical uniquely oriented polarized connecting hole in a correctly oriented adjacent ellipsoidal element, without either ellipsoidal element being removed from its correct gravity stacked position on the gravity tray, with a special torsion spring friction coupling device with the aid of a special torsion spring friction coupling insertion tool;

said six uniquely oriented polarized connecting holes allowing a similarly oriented corresponding ellipsoidal element to optionally be connected to each polarized end, thus twelve similarly oriented corresponding ellipsoidal elements may optionally be connected to one central corresponding ellipsoidal element in the shape of a simple cuboctahedral type configuration, using special torsion spring friction couplers and a special torsion spring friction insertion tool.

16. An educational toy according to claim 15 wherein ellipsoidal elements of said plurality are connected to form a latticework having a tetrahedral configuration with the cuboctahedral type configuration as a nucleus portion thereof;

and

wherein ellipsoidal elements of said plurality are connected to form a latticework having a five-sided pyramid configuration with the cuboctahedral type configuration as a nucleus portion thereof.

17. An educational toy according to claim 16 further comprising:

a tray for supporting said ellipsoidal elements connected in either configuration;

a side of said either configuration lying on said tray when supported thereby.

18. An educational toy according to claim 17 wherein said tray includes a surface and a walled corner on the surface, said walled corner being characterized by a front vertical wall and a vertical side wall that is perpendicular to said front vertical wall, said surface being inclined toward said walled corner.

19. An educational device according to claim 18 wherein the said tray includes a said vertical side wall that may be positioned at an angle to said front vertical wall.

20. An educational toy according to claim 18 wherein each ellipsoidal element has indicia thereon which orient the ellipsoidal element with relation to the said perpendicular side wall of said walled corner of said tray regardless of which configuration the said ellipsoidal element is in and a second and third indicia thereon which face one direction when said ellipsoidal elements are supported on said tray in one configuration and which face another direction when said ellipsoidal elements are supported on said tray in the other configuration.

21. An educational toy according to claim 20 wherein the indicia on each ellipsoidal element includes a triangle, a square and a circle positioned on each ellipsoidal element;

and

wherein said triangle on each ellipsoidal element lies parallel to said tray surface when said ellipsoidal elements are supported in a tetrahedral configuration; and

wherein said square on each ellipsoidal element lies parallel to said tray surface when said ellipsoidal elements are supported in a pyramid configuration; and

wherein center of said circle points the same away in relation to said perpendicular side wall when said ellipsoidal elements are supported in either the said tetrahedral configuration or the said pyramid configuration.

22. An educational device according to claim 20 wherein the centerpoints of said ellipsoidal elements define spacepoints;

and

wherein said ellipsoidal elements are connected by suitable means while being supported on the said tray so that the spacepoints are characterized by a geometric latticework structure formed of only octahedron sections and tetrahedron sections merged together.

23. A device according to claim 22 wherein a number of spacepoints form a rhombohedron geometric latticework which includes two tetrahedrons and an octahedron positioned therebetween, a face of each tetrahedron lying coextensively against a corresponding face of said octahedron.

24. A device according to claim 23 wherein;

one edge of one tetrahedron with spacepoints numbered 701 and 702 in FIG. 7.0 has been designated the common axis edge,

said edge having a length from corner-to-corner substantially equal to unit distance `D` and the other edge lengths from corner-to-corner substantially equal to the ratio of said unit distance `D` as set forth in Table II Sections (a) through (d), where numbered spacepoints are those in FIG. 7.0.

25. An educational device according to claim 20 wherein said ellipsoidal elements are positioned to form a rhombohedral group with each edge of said rhombohedral group comprising an equal number of said elements, said equal number being at least three, and

from said rhombohedral group forming an "up" tetrahedral group, a "down" tetrahedral group and an octahedral group similar to FIG. 7.0, and

demonstrating that the "up" tetrahedral group merges correctly with the octahedral group in only four unique ways, and

demonstrating that the "down" tetrahedral group merges correctly with the octahedral group in only four unique ways, and

demonstrating that none of the four general faces of the "up" tetrahedral group can be correctly merged with any of the four general faces of the "down" tetrahedral group.

26. An educational device according to claim 25 comprising two said rhombohedral groups, and

from said rhombohedral groups forming two "up" tetrahedral groups, two "down" tetrahedral groups and two octahedral groups, and

demonstrating that none of the four general faces of one "up" tetrahedral group can be merged correctly with any of the four general faces of the other "up" tetrahedral group, or with any of the four general faces of the "down" tetrahedral groups, and

demonstrating that none of the four general faces of one "down" tetrahedral group can be merged correctly with any of the four general faces of the other "down" tetrahedral group, or with any of the four general faces of the "up" tetrahedral groups, and

demonstrating that none of the eight general faces of one octahedral group be can be merged correctly with any of the eight general faces of the other octahedral group, thus

demonstrating that twinning of the general latticework structure occurs when a general face of one tetrahedral group is merged with a similar general face of an essentially similar second tetrahedral group, and

demonstrating that twinning of the latticework structure occurs when a general face of one octahedral group is merged with a similar general face of an essentially similar second octahedral group.

27. A device according to claim 15 wherein said three orthogonal axes of symmetry are of such lengths that the center-to-center distances of the ellipsoidal elements are substantially equal to the ratios as set forth in Table I Sections (a) through (d), where the ellipsoids in Table I are as shown in FIG. 4.2.

28. An educational device according to claim 27 wherein said three orthogonal axes of symmetry are of such lengths that the center-to-center distances of the ellipsoidal elements as shown in FIG. 4.2, for the "Rhombus 30" ellipsoid set are as follows:

401 to 402 and 403 to 421 are dimensions substantially equal to the unit distance `D`, and

401 to 421 and 403 are dimensions substantially equal to 1.61803 times the unit distance `D`, and

401 to 403 and 402 to 421 are dimensions substantially equal to 1.47337 times the unit distance `D`, and

are of such lengths that the center-to-center distances of the ellipsoidal elements as shown in FIG. 4.2, for the "Isosceles 60" ellipsoid set are as follows;

401 to 402 is a dimension substantially equal to the unit distance `D`, and

401 to 403 and 403 to 402 are dimensions substantially equal to 0.89800 times the unit distances `D`, and

401 to 421, 402 to 421 and 403 to 421 are dimensions substantially equal to 1.40126 times the unit distance `D`, and

are of such lengths that the center-to-center distances of the ellipsoidal elements as shown in FIG. 4.2, for the "Edge 60" ellipsoid set are as follows;

401 to 402 is a dimension substantially equal to the unit distance `D`, and

403 to 421 is a dimension substantially equal to 1.53884 times the unit distance `D`, and

401 to 421 and 421 to 402 are dimensions substantially equal to 1.40126 times the unit distance `D`, and

401 to 403 and 403 to 402 are dimensions substantially equal to 0.95106 times the unit distance `D`.

29. An educational toy according to claim 15 wherein the set comprises thirteen spheres arranged in a cubotahedron configuration of spheres.

30. An educational toy according to claim 15 further comprising:

a first plurality of twenty-two separate spheres stackable with the cuboctahedron configuration to form a regular tetrahedron configuration.

31. An educational toy according to claim 30 further comprising:

a second plurality of seventeen separate spheres stackable with the cuboctahedron configuration to form a regular pyramid configuration with congruent sides.

32. An educational device for teaching chracteristics of imaginary thirteen nonparallel plane latticework structure comprising:

a plurality of similarly dimensioned matching sets of corresponding tetrahedral and octahedral structural elements, each said matching set consisting of an `up` tetrahedral element, a matching `down` tetrahedral element and a matching octahedral element;

each said matching set being dimensionally characterized by one edge of the base of the `up` tetrahedral being marked as the common axis with a suitable similar indicia indicating the correct orientation or bearing of said edge of said matching set, said edge having a length from corner-to-corner designated a unit distance `D` and the other edge lengths from corner-to-corner designated as a ratio of said unit distance `D` substantially as set forth in Table II Sections (a) through (d), where numbered spacepoints are those in FIG. 7.0;

each face of said matching set being marked with suitable similar indicia indicating the correct orientation of that face in relation to its corresponding face on the appropriate opposite matching structural element of said set, in an imaginary thirteen nonparallel plane latticework structure; and

each face of said matching set being fit with suitable means to attach said face to either an appropriate congruent corresponding face on a matching opposite structural element of said set or of a similar set, when no twining is occurring in the latticework structure; and

each face of said matching set being fit with suitable means to attach said face optionally to a congruent face on a similar matching structural element of said set or of a similar set when twinning of the common latticework is being demonstrated.

33. An educational device according to claim 32 wherein the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Rhombus 30" tetrahedron and octahedron set are as follows:

701 to 702, 703 to 721, 704 to 722, 723 to 724, 803 to 804, 804 to 822, 822 to 821 and 821 to 803 are dimensions substantially equal to each other, and

701 to 721, 702 to 703, 704 to 724, 722 to 723, 802 to 803, 803 to 823, 823 to 822 and 822 to 802 are dimensions substantially equal to each other, and

701 to 703, 702 to 721, 704 to 723, 722 to 724, 802 to 804, 804 to 823, 823 to 821 and 821 to 802 are dimensions substantially equal to each other, and

where thirty corner spacepoints numbered 802 in FIG. 7.0 can be merged together in one point making solid around said one point, and

the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Isosceles 60" tetrahedron and octahedron set are as follows;

701 to 702, 723 to 724, 803 to 804 and 821 to 822 are dimensions substantially equal to each other, and

701 to 703, 703 to 702, 723 to 722, 722 to 724, 803 to 802, 802 to 804, 821 to 823 and 823 to 822 are dimensions substantially equal to each other, and

701 to 721, 702 to 721, 703 to 721, 722 to 704, 723 to 704, 724 to 704, 802 to 821, 821 to 803, 803 to 823, 823 to 804, 804 to 822 and 822 to 802 are dimensions substantially equal to each other, and

where sixty corner spacepoints numbered 721 can be merged together in one point making a solid around said one point, and

the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Edge 60" tetrahedron and octahedron set are as follows;

701 to 702, 723 to 724, 803 to 804 and 821 to 822 are dimensions substantially equal to each other, and

703 to 721, 704 to 722, 803 to 821 and 804 to 822 are dimensions substantially equal to each other, and

701 to 721, 721 to 702, 723 to 704, 704 to 724, 803 to 823, 823 to 804, 821 to 802 and 803 to 822 are dimensions substantially equal to each other, and

701 to 703, 703 to 702, 723 to 722, 722 to 724, 803 to 802, 802 to 804, 821 to 823 and 823 to 822 are dimensions substantially equal to each other, and

where sixty corner spacepoints numbered 721 can be merged together in the point making a solid around said one point.

34. An educational device according to claim 32 wherein the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Rectangular Rotation" tetrahedron and octahedron sets are as follows:

701 to 702, 703 to 721, 704 to 722, 723 to 724, 803 to 804, 803 to 821, 804 to 822 and 821 to 822 are dimensions substantially equal to each other, and

703 to 701, 703 to 702, 721 to 701, 721 to 702, 722 to 723, 722 to 724, 704 to 723, 704 to 724, 823 to 803, 823 to 804, 823 to 821, 823 to 822, 802 to 803, 802 to 804, 802 to 821 and 802 to 822 are dimensions substantially equal to each other, and

where a given whole number of three or nore corner spacepoints numbered 802 in FIG. 7.0 can be merged together with two times the said given wholenumber of corner spacepoints numbered 701 in FIG. 7.0 in one point making a solid around said one point, and

the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Triangular Rotation" tetrahedron and octahedron sets are as follows;

701 to 702, 702 to 703, 703 to 701, 723 to 724, 724 to 722, 722 to 723, 821 to 822, 822 to 823, 823 to 821, 802 to 803, 803 to 804 and 804 to 802 are dimensions substantially equal to each other, and

721 to 701, 721 to 702, 721 to 703, 704 to 722, 704 to 723, 704 and 724, 802 to 821, 802 to 822, 803 to 831, 803 to 823, 804 to 822 and 804 to 823 are dimensions substantially equal to each other, and

where a whole number of corner spacepoints numbered 721 can be merged together in one point making a solid around said one point, and

the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "Rectangular Ellipsoid" tetrahedron and octahedron sets are as follows;

701 to 702, 723 to 724, 821 to 822 and 803 to 804 are dimensions substantially equal to each other, and

721 to 703, 704 to 722, 803 to 821, and 804 to 822 are dimensions substantially equal to each other, and

721 to 701, 721 to 702, 703 to 701, 703 to 702, 722 to 723, 722 to 724, 704 to 723, 704 to 724, 802 to 821, 802 to 822, 802 to 803, 802 to 804, 823 to 821, 823 to 822, 823 to 803 and 823 to 804 are dimensions substantially equal to each other, and

where a first given whole number of three or more corner spacepoints numbered 823 in FIG. 7.0 can be merged together with two times the said first given whole number of corner spacepoints numbered 721 in FIG. 7.0 in one point making a solid around said one point, and

where a different second given whole number of four or more corner spacepoints numbered 823 in FIG. 7.0 can be merged together with two times the said second given whole number of corner spacepoints numbered 701 to FIG. 7.0 in a second point making a solid around said second point.

35. An educational device according to claim 32 wherein the edge distances between the numbered corner spacepoints in FIG. 7.0 for the "General Ellipsoid" tetrahedron and octahedron sets are as follows:

701 to 702, 723 to 724, 803 to 804 and 821 to 822 are dimensions substantially equal to each other, and

701 to 703, 722 to 724, 821 to 823 and 802 to 804 are dimensions substantially equal to each other, and

702 to 703, 722 to 723, 802 to 803 and 822 to 823 are dimensions substantially equal to each other, and

701 to 721, 704 to 724, 802 to 822 and 803 to 823 are dimensions substantially equal to each other, and

702 to 721, 704 to 723, 802 to 821 and 804 to 823 are dimensions substantially equal to each other, and

703 to 721, 704 to 722, 803 to 821 and 804 to 822 are dimensions substantially equal to each other, and

where corners of four tetrahedrons and corners of three octahedrons may be merged together at one point making a plane surface passing through said one point, said corners being numbered 701, 702, 703, 704, 802, 803 and 804 in FIG. 7.0.

36. An educational method comprising the step of:

demonstrating the commonality of internal lattice structure between equal diameter spheroids arranged to form (a) a regular tetrahedron configuration and (b) a pyramid configuration having (i) an equilateral base and (ii) four congruent sides, when such configurations are extended in space;

wherein the commonality demonstrating step includes the steps of;

forming the tetrahedron configuration of spheroids and the pyramid configuration of spheroids to have the same number of layers; and

coupling at least one side of the pyramid configuration to a corresponding one of the tetrahedron faces comprising the step of defining the spheroids along each said at least one side of the pyramid configuration to be the spheroids along each corresponding tetrahedron face.

37. An educational method according to claim 36 wherein commonality demonstrating step comprises the further step of:

dividing the pyramid into four equal 1/8th octahedron sections with two planes passing diagonally across and perpendicular to the pyramid base, spheroids common to a plurality of the 1/8th octahedron sections being represented in each such 1/8th octahedron section as whole spheroids.

38. An educational method according to claim 37 wherein the coupling comprises the further step of:

merging each pyramid side of each 1/8th octahedron section to a corresponding tetrahedron face.

39. An educational device for teaching characteristics of latticework structure comprising:

sets of structural members of suitable material, comprising a plurality of similarly dimensioned tetrahedral structural members and a plurality of similarly dimensioned octahedral structural members, where the ratio of said structural members in said sets is essentially two tetrahedral structural members for each octahedral structural member; and

said sets of structural members having a designated common axis edge on one edge of the tetrahedrons, which edge has a length substantially equal to the unit distance `D`; and

said sets of structural members having corner-to-corner dimensions substantially as set forth in Table II Sections (a) through (d); and

an additional plurality of corresponding structural members comprising one-half octahedron structural members made by passing a single plane through any one of the three planes with four spacepoints therein, resulting in a structural member containing five spacepoints of the original six spacepoints of the corresponding octahedron structural member; and

an additional plurality of corresponding structural members comprising first one-quarter octahedron structural members made by passing two planes through any two of the three planes with four spacepoints therein, resulting in a structural member containing four spacepoints of the original six spacepoints of the corresponding octahedron structural member; and

an additional plurality of corresponding structural members comprising second one-quarter octahedron structural members made by passing two planes through any two opposite spacepoints, with each plane passing through a different third spacepoints equidistance on the edges made by the other four spacepoints of the original six spacepoints of the corresponding octahedron structural member, resulting in a structural member containing three spacepoints of the original six spacepoints of the corresponding octahedron structural member; and

an additional plurality of corresponding structural members comprising first one-eighth octahedron structural members made by passing three planes through the three planes with four spacepoints therein, resulting in a structural member containing three spacepoints of the original six spacepoints of the corresponding octahedron structural member; and

an additional plurality of corresponding structural members comprising one-half tetrahedron structural members made by passing a plane through two of the four spacepoints of the tetrahedron and a third spacepoint equidistance on the edge defined by the two remaining spacepoints of the said corresponding tetrahedron structural member, resulting in a structural member containing three spacepoints of the original four spacepoints of the corresponding tetrahedron structural member; and

said structural members having suitable means for connecting congruent faces to each other; and

said structural members having suitable markings which indicate the proper orientation of each face of each structural member in relation to the face of each other structural member.

40. An educational device according to claim 39 demonstrating the shape of the effective ellipsoid of influence in imaginary thirteen nonparallel plane space latticework structure when said ellipsoid of influence is expanded into the interstices therebetween wherein;

an additional plurality of corresponding structural members comprising said second one-eighth octahedron structural members made by passing four planes that are parallel to the original four sets of parallel planes of the original octahedron and equidistance between those corresponding sets of parallel planes, resulting in six structural members each containing one spacepoint of the original six spacepoints of the corresponding octahedron structural member; and

an additional plurality of corresponding structural members comprising one-quarter tetrahedron structural members made by passing six planes into the center of a corresponding tetrahedron structural member where each plane passes through a point on each edge equidistance from first two spacepoints on ends of said edge and tangent to the corresponding ellipsoids touching at said point, each said plane stopping when it intersects another said plane, resulting in four structural members each containing one spacepoint of the original four spacepoints of the corresponding tetrahedron structural member; and

said structural members having suitable means for connecting congurent faces to each other; and

said structural members having suitable markings which indicate the proper orientation of each face of each structural member in relation to the face of each other structural member.

41. An educational device according to claim 40 wherein:

an additional plurality of corresponding structural members comprising merged combinations of two or more tetrahedral and octahedral structural members where no twinning has occurred.

42. An educational device according to claim 41 wherein:

an additional plurality of corresponding structural members comprising merged combinations of two or more tetrahedral and octahedral structural members where twinning is occurring.

43. An educational method comprising the steps of:

demonstrating the commonality of internal lattice structure between equal diameter spheres arranged to form (a) a regular tetrahedron configuration and (b) a pyramid configuration having (i) an equilateral base and (ii) four congurent sides, when such configurations are extended in space;

wherein the commonality demonstrating step comprises the further steps of;

packing equal diameter spheres relative to each other to form a cuboctahedron configuration;

orienting the spheres in the cubotahedron configuration in a first prescribed manner;

selectively stacking additional equal diameter spheres relative the spheres that are packed and oriented in said first prescribed manner to form a regular tetrahedron configuration;

44. orienting the spheres in the cuboctahedron configuration in a second prescribed manner;

and

47. A method according to claim 44 wherein said positioning step includes the step of:

gravity stacking a plurality of at least substantially similarly dimensioned, similarly oriented ellipsoidal elements, wherein each ellipsoidal element is one of the structural members and the centerpoint of each ellipsoidal element is a spacepoint in the latticework.

45. selectively stacking additional equal diameter spheres relative to the spheres that are packed and oriented in said second prescribed manner to form a pyramid configuration having a four-sided equilateral base and four equal sides.

46. A method of teaching characteristics of latticework structure comprising the steps of:

demonstrating the commonality of lattice structure of (a) latticework extending from a basic tetrahedron first configuration and (b) latticework extending from a basic pyramid second configuration which has a (i) four-edged base and (ii) four sides that extend from the base and meet at a point, said demonstrating step including the steps of;

positioning a plurality of structure members relative to each other to define spacepoints in a latticework arranged in one of the two basic configurations;

adding structural members to expand the latticework arranged in said one basic configuration; and

removing structural members from the expanded latticework to define spacepoints in a latticework arranged in the other of the two basic configurations.

49. An educational device according to claim 46 wherein said sturctural members are positioned to form a helix.

50. An educational device according to claim 46 wherein said structural members are positioned to form a spiral.

51. An educational device according to claim 46 wherein said structural members are positioned to form a helical like spiral.

52. An educational device according to claim 46 wherein said structural members are positioned to form a tetrahedron.

53. An educational device according to claim 46 wherein said structural members are positioned to form an octahedron.

54. An educational device according to claim 46 wherein said structural members are positioned to form a rhombohedron.

55. An educational device according to claim 46 wherein said structural members are positioned to form a geometrical configuration.

56. An educational device according to claim 46 wherein said structural members are positioned to form a three dimensional geometric form.

58. An educational device according to claim 55 wherein the elements have a complex ellipsoidal shape where all planes through the center of said complex ellipsoidal element cut the surface of element in the form of segments of a circle or segments of an ellipse merged together so that a line tangent to the surface of the element is also tangent to both segments where the segments meet.

48. An educational device for teaching characteristics of latticework structure comprising:

sets of structural members of suitable material, comprising a plurality of similarly dimensioned tetrahedral structural members and a plurality of similarly dimensioned octahedral structural members, said structural members having congruent faces and means for connecting congruent faces of said structural members together.

57. An educational device for teaching characteristics of imaginary thirteen nonparallel plane latticework structure comprising:

a plurality of ellipsoidal elements of substantially equal size and shape with similar dimensions and indicia, and

each said element having a common axis essentially passing through its center with a suitable common axis indicia at one end, and

each said element having a suitable rotation indicia placed perpendicular to said common axis on the surface of said element, and

demonstrating that when said elements are positioned with a similar bearing with one end of each common axis touching the oppostie end of the common axis of an adjacent said element, and

where all common axes are parallel and all rotational indicia have the same bearing, when twinning does not occur, the centers of said elements define one unique latticework structure, wherein

twinning does not occur when elements are oriented with the same bearing and positioned so their common axes are touching, and

first three equal sets of elements positioned along their common axes are merged together so that each element is touching three other elements, and

each additional element is positioned touching at least four other elements where said four other elements are in a plane, or

each additional element is positioned touching at least one other common axis, or

each additional element is positioned touching at least three other elements where said three other elements are touching each other in a plane, and no other element is already touching said three other elements.