Educational device and method

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.

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.

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.

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.

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.

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

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.

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.