Abstract: A mathematical triangle kit designed to teach children and adults mathematical and symmetry skills utilizing various sized patterned blocks. By manipulating the patterned blocks the participant learns mathematical skills, such as fractions, multiplication, trigonometry, and geometry. Additionally, by manipulating the patterned blocks the participant also learns geometric relations, such as mirror images and other symmetry relationships amongst the patterned blocks. In the preferred embodiment, the mathematical triangle kit comprises three sets of various sized and colored right triangles with 30.degree. and 60.degree. bases.

Abstract: A connector body (10) for joining elongated rods or struts (12) for use in creating three-dimensional structures or models is disclosed. The connector body (10) includes a plurality of resilient particles (14) such as spherical balls formed of polystyrene material and a cohering means (16) such as an adhesive compound for cohering the particles (14) to form the connector body. The connector body (10) is highly resilient and crush-resistant and can be easily penetrated by the ends of the elongated rods (12) to form three-dimensional structures. Once the rods (12) are removed from the connector body (10), the connector body immediately returns to its original shape to close the openings formed by the ends of the rods (12).

Abstract: A set of polyhedrons have shapes capable of fitting together, in one or more ways, into a solid geometric shape such as a rectangular solid or more specifically, a cube. The polyhedrons include five-sided polyhedrons made up of a regular tetrahedron and an irregular tetrahedron abutted together as one solid; alternately, the two separate tetrahedra can be included in lieu of one or more of the five-sided polyhedrons, for assembly in the puzzle. The set of polyhedrons includes separate irregular tetrahedra and may include a regular octahedron. Preferably each shape of polyhedron is in a different color. In a preferred embodiment, the polyhedrons are all solid throughout and are of the same density, and that density is preferably the same density as water to enable the teaching of certain relationships. The set of polyhedrons function not only as a puzzle, for fitting into a transparent housing such as a cube, but also for educational purposes in teaching geometry.

Abstract: Kaleidoscopes are used to show solid-appearing images of the Platonic and Archimedean polyhedra (except the snub solids) and of the Kepler-Poinsot stellations. The polyhedra are divided into families related by possessing the same planes of mirror and rotational symmetry, thus using reflectors consisting of three to five mirrors meeting at vertices with specified angles, and corresponding fractions of the solids, such as an octant of the cube for the whole. The fractions may be truncated to form elements representing other members of the families. Slices formed by successive truncations may be superposed to make smaller the elements required. The stellations result from the insertion of the star's "rays" or fractions into reflectors identical with those above. All images appear as solids, not just vertex points, and are viewable over wide angles. The elements are much smaller than the polyhedra, and the reflectors can be folded and/or disassembled for ease of storage and transportation.

Abstract: A geoboard has a board member with a plurality, advantageously four edges. An array of holes which is preferably in the form of a matrix, is provided in the board member for receiving slidably mounted push-up pins. Each push-up pin has upper and lower positions and the pins are arranged in the matrix for engagement by an elastic band to form shapes on the board member. Each of the edges includes spaced-apart notches for receiving fixed slider pins which extend in a row on a slider. Each slider is slidably mounted along one of the edges for extending the matrix of push-up pins.

Abstract: A didactic-educational toy for elementary arithmetic operations includes a plurality of transparent plates. Each of the transparent plates has ten circular orifices. The orifices are distributed symmetrically in two rows. Each row has five of the orifices. Each of the orifices has substantially the same diameter. A plurality of plates each has cylindrical stepped protuberances. Each of the protuberances has a base with a diameter corresponding to a diameter of the orifices of the transparent plates to provide for close-fitting insertion of the base into a corresponding one of the orifices. Each of the protuberances has an upper portion having a diameter smaller than the diameter of its base to facilitate the insertion of the protuberance into a corresponding orifice. The plurality of plates, which have cylindrical stepped protuberances include plates has a different number of protuberances. The surface area of each plate is substantially proportional to the number of protuberances.

Abstract: A system for teaching proofs, including a set of playing cards and a playing field electronically displayed on a computer game screen. The playing field includes two boxes labelled "GIVEN" and "CONCLUSION" for entry of a premise and a conclusion from a theorem (or other problem). By selecting from a certain menu or submenu contained in a window, a card may be reviewed. To set up the playing field, a mathematical statement, displayed on a set-up card of a group of set-up cards containing each statement from the universe of statements known, is entered into the boxes. The statements may be custom labelled. Geometric figures associated with the theorem may also be electronically drawn on the screen by a user to complete the set-up. After set-up is complete, a user then chooses from a set of playing cards, each card displaying a specific mathematical concept from the universe of mathematical concepts such as definitions, postulates, constructions, properties and theorems, and places it on the playing field.

Abstract: An apparatus for teaching polynomial expressions includes an arrangement of groups of rows and columns that represent the variables of factors of a polynomial expression. Each group of columns or rows has a different width or height, respectively, and represents a different variable in the polynomial expression. The apparatus enables an algebra student to visualize the rules that apply to polynomial expressions. In one embodiment, the rows and columns are defined by a plurality of pegs or nails fixed to a supporting member. Each factor of the polynomial expression is represented by isolating the variables of the factors by extending an elastic member around the appropriate pegs. The intersection of the two isolated factors represents the product of the factors.

Abstract: A visual aid teaching device for translating one or more superimposed picture images in a linear path at different positions with respect to a stationary underlay picture includes as basic components: a pair of edge strip members, each embodying two or more channel tracks; a transparent, or opaque, rectangular flat surface member snugly mounted on the edge strips through their channel tracks to assemble the body device; sets of layers, each including a stationary underlay picture member and one or more superimposed picture image members. Both members may include algebraic graphs or circles divided into sets of sectors. The layer members can be mounted on the other channel tracks. Algebraic problem solving of compound inequalities in one variable can be demonstrated algebraically along with their graphic solution sets simultaneously by means of translating one or more superimposed graphs at different positions with respect to a set of number line graphs.

Abstract: This present invention relates to displaying devices for instructive purposes. One object of this invention is to provide a composition of translations or a combination of rotation and translations in two orthogonal dimensions, to locate superimposed picture images to any selective location with respect to stationary pictures. The devices of this present invention are used to visually compare intelligence or information in the form of pictures, diagrams, or graphs for instructive reasons.Another object is to provide animated motion of pictures, diagrams, or graphs for teaching aid in education and in mathematics in particular. This invention provides animated transformation of geometric diagrams or Algebraic graphs to visually demonstrate the proofs of geometric theorems or to find instantaneous solutions of geometric problems or algebraic problems graphically for curricula in geometry and algebra.

Abstract: A light table includes a housing extending in a horizontal direction having legs extending downwardly therefrom. The housing defines X- and Y-axes and has an X-Y grid pattern formed thereon and visible from above the housing. A lighting system is used to illuminate the grid pattern. A frame extends vertically upwards from the housing and defines a Z-axis having an X-Z grid pattern formed thereon. A second lighting system illuminates the grid pattern on the vertical frame.

Abstract: A geometry board having pegs arranged on its top face for the demonstration of planar geometric figures by stretching of elastic bands about the pegs. The disclosed board is of clear injection-molded plastic and has a square face with the pegs arranged in a grid on the face including along edges of the board. Pegs along the edges are in the shape of semi-cylinders and the arrangement is such that a pair of boards may be located side-by-side so that the semi-cylinders are paired up so that each pair of semi-cylinders forms a single cylinder. Pegs located at the corners of the board are in the shape of quarter-cylinders so that when four corner pegs are located at the center of four boards laid side-by-side the four quarter-cylinders form a singe cylinder. When four boards are assembled together a Cartesian coordinate system is obtain with x- and y-axes along adjacent edges of the boards and point (0,0) located at the intersection of all four boards.

Abstract: A device and method for illustrating geometric shapes are disclosed which enables individuals to study and visualize the interrelation between geometric shapes and more particularly complementary geometric shapes such as tetrahedrons. The apparatus includes a plurality of tubes that pass through a central support member. Cords pass through the tubes, each cord having its ends connected, forming a closed loop. The tubes are movable within the support member. As the tubes are manipulated, the size and geometry of the visualized shapes are altered. In one embodiment, four tubes and three cords define two complementary tetrahedrons. When the tubes are manipulated to expand one tetrahedron, the complementary tetrahedron shrinks.

Abstract: The pictorial image transforming manipulatives are instructional visual aid devices adapted for use to demonstrate visually the applications of deductive reasoning in proving most of the geometry theorems in conjunction with a geometry course. The manipulatives can also be used to display visually many graphs which represent algebraic linear equations and inequalities in two variables, and compound inequalities on a number line. These applications of mathematical systems for demonstrated algebraic linear graphs, and other graphs, are designed in conjunction with algebra textbooks.Each device uses one or more transparent overlays which rotate, translate, translate and rotate, flip over, or flip over and rotate to another position relative to a stationary underlaid plate. The manipulative devices are adapted for use on the overhead projector or for use in direct demonstration without a projector. These devices can be produced in small sizes for student use or in large blackboard sizes.

Abstract: A geometric block system for constructing a regular rhombic dodecahedron having twelve identical rhombic faces, the system consisting of eight identical first blocks each being one-quarter of a regular tetrahedron and eight identical second blocks each being one-eights of a regular octahedron. The regular tetrahedron has six edges of length "a" and four identical equilateral triangular faces with sides of length "a". Each first block has one cubic unit of volume and has an apex at a point corresponding with the center of gravity of the tetrahedron and has first, second, third and fourth triangular faces. The first face is equilateral triangular with edges of length .intg.a"; the second, third and fourth faces are isosceles triangular with one edge of length "a" and two edges of length "b" equal to a .sqroot.6/4. The regular octahedron has eight edges of length "a" and eight identical equilateral triangular faces with sides of length "a".

Abstract: A mathematical teaching aid or game comprising a background grid having components and subcomponents each positioned within individual cells of the grid so that many mathematical arrangements and concepts can be displayed. Each component has a face color from a set of colors and contains on its face the outline of a geometric shape from a set of geometric shapes. Each component represents a unique pairing of color and shape outline. Each subcomponent has a shape congruent to the shape outline from the set of shapes and matches exactly one component with respect to color and shape outline. The components are mounted upon the grid cells and the subcomponents can be mounted upon either a grid cell or upon a corresponding shape outline.

Abstract: An educational board for use in demonstrating mathematical principles has a surface marked with a circle having its circumference marked with gradations indicating 360 degrees. The board is provided with pins to mark any angular displacement along the circumference and connecting elastic bands which are stretched around the pins to create shapes inscribed in the circle.

Abstract: An electromechanical demonstrator board of one or more of the six trigonometric functions. The board is powered electrically by a battery and mechanically by a hand crank which drives a pointer and contact arm. The circuits include light emitting diodes (LEDs) arranged into three groups. The first group represents a unit circle. The second group is on a vertical segment, and the third group is on the path of the function and the horizontal axis. The first group of LEDs indicates particular angle measures on the unit circle. In the second group, vertically oriented LEDs indicate harmonic motion. The third group of LEDs demonstrates a graph of the trigonometric function and the measure of linear movement related to rotation on the unit circle.

Abstract: A supplementary teaching instrument based on mathematical basic theories and principles as well as child psychology. The invention employs a number of rectangular blocks of a prescribed shape which occupy a predetermined area when assembled together, and a corresponding area of triangular shaped blocks of various sizes and shapes. In addition to creating artistic designs by different arrangements of the blocks which may be of different colors, the rectangular blocks can be used in the fashion of a domino game, and the dimensional relationship between the triangular blocks and the rectangular blocks teach the basic concepts of mathematics including addition, substraction, multiplication, fractions, areas, and the like.

Abstract: A toy is made up of a number of different elements which fit together in a particular manner to form a spherical body. A first set of elements are each of a pyramid shape with a hexagonal cross-section and a second set of elements are each of a pyramid shape with a pentagonal cross-section. The respective elements fit together in a particular manner to form a spherical body and have interfitting tongue and groove connectors.

Abstract: A fractal mathematics learning kit includes a plurality of boards each in the shape of an equilateral triangle having defined thereon a pattern of ten smaller equilateral triangles, and a plurality of manipulative elements made of one or more connected equilateral triangles which are attached to the equilateral triangles defined on the boards. A set of tokens thick enough to stand on an edge and comprising combinations of equilateral triangles to represent numbers is also included. Also included in the kit is a mat defining rows and columns of fractal representations of numbers by which various mathematical operations can be understood. A set of nesting pyramids of graduated sizes representing numbers of magnitudes generally corresponding to the sizes is also provided, as are pyramids of different sizes which can be stacked through the use of trays and transparent covers. The kit includes a work book and a user's manual.

Abstract: A series of interrelated solid, geometric shapes having informational - processing applications. Each solid, geometric shape may be assigned a specific meaning; additionally, any one solid, geometric shape may be assigned several specific meanings by changes of color, braille, scoring, texture, and/or tone (sound). Means for connecting different solid, geometric shapes are provided and are called connectors, which may or may not be assigned specific meanings or several meanings by changing the solid, geometric shape, color, braille, scoring, texture, and/or tone (sound). The series of interrelated solid, geometric shapes may be used for (1) physiology--fine motor coordination, visual or auditory/tactile perception, and joint hemispherical stimulation of the cerebral cortex and (2) communication--language, history, art, computer programming, computer processing (grammatical and parallel), and abstract thinking.

Abstract: A set of building blocks having two subsets of rhombohedral blocks (B,Y) having respectively dihedral angles of 72.degree. and 36.degree. so that the faces of both subsets of blocks are identical. Each of the faces incorporates magnets (11) whereby juxtaposed faces of any two blocks will stick together magnetically in a predetermined angular orientation.

Abstract: The present invention relates to an improved rotational movement training device which includes a mounting board and a plurality of rotation devices which, when mounted on a mounting board, provide a training device which permits a user through experimentation to develop mathematical expressions and mechanical systems from elementary scientific facts and basic mathematics. The rotational devices includes gears or wheels of different diameters, pistons, torque levers, force and load pans, fulcrum-levers and devices to interconnect the wheels and pistons such as levers, belts, and adjustable spacers. The devices may be used in various combinations to develop and demonstrate mechanical movement concepts and expressions.

Abstract: An educational aid, comprising a figure representing an animate object. A plurality of first enhancing means are provided which are adapted to attach magnetically to the figure. One surface of the first enhancing means bears representation of at least one teach object. A plurality of second enhancing means is provided, which are adapted to magnetically attach to the figure, wherein the second enhancing means relates to a feature of the teaching object.

Abstract: An educational device is set forth in application for the training and education of young children or of mentally deficient individuals. A background board has positioned thereon a plurality of removable pegs. A matrix of pegs is utilized in the body of the board for the orientation of pre-selected geometrical shapes of varying colors. A plurality of pegs is positioned in overlying relationship to the matrix for indication of a pre-selected number of the varying geometrical configurations. Spinners may be utilized in the random selection of a geometrical configuration to be utilized and a second spinner to be implemented for the random selection of a coloration of the geometrical shape. Accordingly, association of colors and geometrical configurations is available for educational purposes as set forth above.

Abstract: An educational game which has predetermined polyhedral bodies. The dimensions of the edges of the polyhedral bodies are ratios substantially equal to 1 and to a whole power of .tau., with ##EQU1## This game also includes (a) at least one polyhedral body for defining a tetrahedral volume;(b) at least one polyhedral body for defining a pyramidal hexahedral volume;(c) at least one polyhedral body for defining a bipyramidal heptahedral volume; and(d) at least one polyhedral body for defining an octahedral volume.The polyhedral bodies of the game allow a non-periodical filling of the space, the formation of homothetic volumes of the volumes and of regular dodecahedral volumes.

Abstract: A geometrical structural system is made up of a plurality of nodes and shape-coded connectors extending therebetween, each node having a plurality of outer polygonal elements. The outer edges of each element are bordered by end edges of other elements and each element has an opening therethrough corresponding to the outer side edges of each element. Each opening extends radially into a hollow space centrally of each node. The connectors are elongated and have opposed connecting ends with a cross-sectional configuration corresponding to a cross-sectional configuration of an opening in one of the element faces for insertion therein.

Abstract: The play set having a plurality of pieces having fixed shape, each of which is ideally made up of a number of variously disposed cubes, with at least a face in common, and at least a piece of variable shape and actually made up of a number of cubes variously matchable between them for taking up a number of shapes, always with a face in common; said pieces of fixed and variable shape being combinable between them to generate various spatial patterns.

Abstract: A planar member 21, is pivotally assembled to a transparent planar member 22, at pivot point 23. On the planar member 21, are the calibrated circle 24, the cosine/secant scale 25, and the sine/cosecant scale 26.On the transparent member 22, are the sine/cosine cursor circle 27, the tangent/cotangent scale 28, and the arrow head 29.For any relative position of the two members, the arrow head 29, points to an angle. Each of the six trigonometric functions of that angle is read where the appropriate scale is intersected by another line.FIG. 2, shows the device set at 150 degrees as an example. The sine and the cosine of 150 degrees are read at intersections 33 and 34 respectively. The secant and the tangent at intersection 31. The cosecant and cotangent at 32. The sign of any cotangent reading needs to be reversed.

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.

Abstract: Disclosed are methods for structurally differentiating polynomial functions using parallelogrammic elements. The methods include representing a first ordered pair defined by the polynomial function as a construction of such structural elements. Second or sequent sets are also similarly constructed for an ordered pair defined by a different variable value. The resulting structural sets are compared to determine differences and the differential is expressed either directly or after dividing by the associated change in the variable of the polynomial function used to construct the two or more sets of elements.

Abstract: A set of didactic blocks to be used by children is provided and consists of a plurality of different shaped geometric solid members and a plurality of indicia associated with the geometric solid members to stimulate artistic creativity and at the same time teach children mathematics, science, language and the like when the blocks are manipulated in play.

Abstract: An amusement device comprises a solid cube which may be disassembled into a plurality of blocks of differing geometric shapes wherein each of the geometric shapes is formed from one or more modular units. Each modular unit comprises an isosceles right triangular prism having a triangular face formed by two legs each of which has a length A and which meet at a right angle, and a hypoteneuse which has a length B, said modular unit having a depth which is equal to A, and a volume which is equal to C. Each of the differing geometric shapes is formed from one or more modular units and has a volume equal to an integral number times C, and the total volume of said solid cube is equal to 16C.

Abstract: A hollow ball-like construction is disclosed as including a plurality of hollow wedges having a variety of different shapes and angles, which wedges are mounted on a central disc to form a unitary assembly. Cylindrical and spherical wedges of different configurations are utilized to complete the constructions into a plurality of outlines, such as a trapezoid, a rhombus, a square, a triangle, a pentagon, a hexagon and other irregular outlines.

Abstract: The invention is concerned with the technical field of structures adapted to provide entertainment of a didactic character, and in particular with a block subdivided into suitable portions to compose three-dimensional figures. The technical problem to be solved was that of providing a simple structure whereby a very high number of three-dimensional configurations could be obtained, the elements which make up the game being in such mutual relationship as to favor the attainment of such three-dimensional configurations.

Abstract: A teaching tool is provided in the form of a glove with a plurality of tags which are removably attachable to the glove. Preferably the tags are provided with indicia such as letters, numbers, words, shapes and such which can be placed on or removed from the glove as part of individual or group learning exercises for small children.

Abstract: A structural element in rectangular form folded along its longitudinal center forming a truss element in triangular faced polyhedrals when end edges of the structured element are connected to the corresponding adjacent, respective, end edges of like structural elements in an assembled polyhedral. The fold in the structural element assumes a dihedral angle well under 180.degree., approximating 110.degree., with the truss element used in forming a four triangular faced tetrahedron, 90.degree. with the truss element used in a cube, although this is an unstable structure in not presenting the structural shape integrity attained inherently with truss elements used in triangularly faced polyhedrals. Further, the structural element assumes a dihedral angle approximating 75.degree. with the truss element used in forming an eight triangular faced octahedron, and approximately a 42.degree. fold in the truss elements forming a twenty triangular faced icosahedron.

Abstract: A plural-loop Mobius strip loop puzzle having multiple twist component loops which are linked with each other and which have mating continuous edges with associated edge fasteners to permit assembling and disassembling a single composite Mobius strip loop.

Abstract: A set of generally flat, geometric figure building elements is disclosed, particularly (but not necessarily) for use in a geometric puzzle. The set combines an uneven number of pieces or elements, of which one type is square-shaped and the other types are right-angled isosceles triangles, one of which has the sides equal to the sides of the square pieces, while the other type is of the shape of right-angled triangles whose bases are of the same length as the sides of the square pieces. The puzzle produces advance in that it combines extreme simplicity of the pieces with the possibility of a wide variety of difficulty in assembling different shapes from the entire set. In a preferred embodiment, at least some of the pieces display a centrally located dot-like figure in one surface only thereof, to enable the creation of animal or man-like figures in which the dot presents representation of the eye, or to facilitate recognition of a particular piece in an overall shape to be solved.

Abstract: a plurality of identically shaped tiles having an odd number of sides may be used to form a periodic or non-periodic pattern when covering a plane surface.

Abstract: A series of interrelated sets of tetrahedron blocks. Each set comprises twelve blocks capable of assembly into a rectangular parallelepiped using all twelve blocks, and is also capable of assembly into an eight-block pyramid and a four-block tetrahedron. The pyramid and parallelepiped of all sets are the same height. The tetrahedrons are preferably hollow and each of them has a magnet for each face, e.g., affixed to the interior walls of its faces, the magnets being so polarized that upon assembly into a cube or pyramid, the magnets of facing faces attract each other. Preferably, the blocks are colored in such a way that faces of the same size and shape are colored alike and each size and shape has a different color.

Abstract: A series of interrelated sets of tetrahedron blocks. Each set is capable of assembly into a cube with all the cubes being identical in size. Typically, there are at least three such sets, though there may be more; and when there are three sets, for example, one set contains twice as many tetrahedron blocks as the second set and four times as many as the third set. The tetrahedrons are preferably hollow and each of them has a magnet for each face, e.g., affixed to the interior walls of its faces, the magnets being so polarized that upon assembly into a cube or pyramid, the magnets of facing faces attract each other. Preferably, the blocks are colored in such a way that faces of the same size and shape are colored alike and each size and shape has a different color.

Abstract: The apparatus is used as a teaching aid for arithmetic, metric and analytical geometry and elementary algebra, and is formed by a cubic block array comprising a plurality of different size blocks arranged in rows and columns. The cubic block array has a base array of ten-by-ten blocks commencing with a one centimeter block and progressing in x and y rows with increasing length blocks (1 cm., 2 cm., 3 cm., etc.), and overlying arrays of the same pattern but progressively increasing in height (1 cm., 2 cm., 3 cm., 4 cm., etc.).

Abstract: A manipulative toy comprising a number of spheres serially attached in a closed loop or open chain, each sphere being attached to the next at a fixed point on its surface by a connector which allows relative rotation of adjacent spheres about a common axis through their centres.

Abstract: The present invention relates to an amusement device which is formed of a plurality of differently shaped modular units which can interfit to form a solid equilateral tetrahedron. Each of the modular units is a single solid piece having a shape which is defined by the integral combination of one or more solid equilateral octrahedrons and one or more solid equilateral tetrahedrons. The modular units can also interfit to form random three-dimensional sculptural shapes.

Abstract: Sets of educational blocks are described wherein special volumetric relationships are combined with visually distinctive geometric shapes. In one set of blocks a common cube is cut into distinctive segments along a single slice to form particular polygons. In another set of blocks a common cube is cut in a manner to provide polyhedra of distinctive appearance with related outer segments used to fill out the common cube. Particular volumetric relationships between the polyhedra and their related segments are described.

Abstract: Sets of educational blocks are described wherein special volumetric relationships are combined with visually distinctive geometric shapes. In one set of blocks a common cube is cut into distinctive segments along a single slice to form particular polygons. In another set of blocks a common cube is cut in a manner to provide polyhedra of distinctive appearance with related outer segments used to fill out the common cube. Particular volumetric relationships between the polyhedra and their related segments are described.

Abstract: An educational toy, teaching device and puzzle block combination comprising a plurality of sets of blocks of decreasing dimensions so related one to another as to complete an overall design. Preferably these comprise three sets of cubes color coded so that the combination defined by the cubes may be realized by assembling the cubes in a particular order. To this end there are seven cubes of a given dimension, seven cubes of an intermediate dimension and eight cubes of a smaller dimension. The cubes define three horizontal planes of decreasing size and three vertical planes of a first orientation and of decreasing size and three vertical planes of a second orientation and of decreasing size. The cubes are colored so as to define a pair of matching patterns in each of the nine planes so defined. Each cube, therefore, will be colored on anywhere from three to six of its sides. In the preferred arrangement the colored patterns are circles and all exposed sides of the fully assembled cubes are plain.

Abstract: A geometrical structural system is made up of a plurality of nodes and shape-coded connectors extending therebetween, each node having a plurality of outer polygonal elements. The outer edges of each element are bordered by end edges of other elements and each element has an opening therethrough corresponding to the outer side edges of each element. Each opening extends radially into a hollow space centrally of each node. The connectors are elongated and have opposed connecting ends with a cross-sectional configuration corresponding to a cross-sectional configuration of an opening in one of the element faces for insertion therein.