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The Vector Equilibrium is part of the Cubic family that includes the Tetrahedron (and star tetrahedron), the Octahedron, the Cube, the 64 Tetrahedron Grid, and the Isotropic Vector Matrix. However - it does not include the 5 symmetry Platonic forms, and the link between them is not obvious. Therefore this model is significant in showing that there is a link - albeit an imperfect one - as 5 VEs do surprisingly form an almost perfect circle. The gap in the ring made by the 5 forms is so small that it is covered up by the thickness of the lines....

One way to portray an extra dimension is to use size. For instance a square inside a larger square with lines joining the vertices is often used to represent a cube, and a cube within a larger cube is often used to represent a hypercube. Here we have a hypercube inside a larger hypercube, and if the corresponding vertices were joined we would have a version of the 5D cube. The Hypercube is the 4 dimensional analog of the cube. For full info on it see the Wikipedia article here. This model is a Toroidal Hypercube inside another Toroidal Hypercube....

  The Stellated Dodecahedron with its 12 stars is one of the most beautiful extensions of a Platonic Solid. It relates to the DNA structure, and of course being pentagonal it is all golden ratio proportions. The 12 points of the stellated dodecahedron form an invisible icosahedron. (We also have a model where the icosahedron is added as well). These are the two 5 symmetry platonic solids. The 5 symmetry of these shapes is what creates the instability that allows life to exist so it is natural that the DNA should be based on them. The five symmetry also means...

Buckminster Fuller gave this geometry the name vector equilibrium because uniquely among 3d forms the distance between its vertices and the center is the same as its edge lengths. Understanding as he did so well that the physical form represented a deeper energetic structure he realised that this form was the most balanced between expansion and contraction, the zero point from which nature creates everything. The equivalent 2d form is the hexagon, and you can find 4 interlocking hexagons in the V.E. This form is one of the 13 Archimedean regular solids, but in many ways it is more primary...

This form is a study of the nature of spacetime itself. It is based on Buckminster Fuller's work with the Vector Equilibrium. If you would like to learn more about geometry and the new physics I highly recommendthe Resonance Projects Delegate Program here   As shown in the image above, space can be tiled with a combination of Vector Equilibriums (aka Cuboctahedrons) and Octahedrons in the spaces inbetween. As Fuller showed using rubber connections at the vertex the cuboctahedron can be collapsed down into the octahedron, so these two forms are intimately related to each other. Above is an animation...

This shape is made from 12 circles that create 12 five pointed stars. It is another variation on the starcage dodecahedral theme. Variations are also here The Cage of Stars ~ by NDV The Angel trap Is a jewel that contains An infinity of stars And if once a spirit Should glance into its depths He will forever remain Lost within its heart For the endless reflections Of time will circle round him And in each face He will find a small part Of the infinite design Like a memory to confound him With impossible meanings Like invisible bars And...

  Each of the lines of an icosahedron has been extended so that the 20 triangles beach becomes a point of a star. These outer points can be linked to form a dodecahedron.  These twin 5 symmetry forms both embody the golden ratio in all their proportions. They are related to the DNA and the process of life, whereas the 3 and 4 symmetry forms are related more to space, time, matter, and energy. The 20 sided icosahedron is one of the 5 Platonic Solids, convex forms that have all their angles and faces equal. The 5 symmetry of these...

Interlocking circles make this lovely form that is the 3 dimensional 'Seed of Life' that is the center of the 3 dimensional Flower of Life.   Related forms available in our shop~ Products related to Flower of life---- Seed of life----Hyperbolic Seed of Life 30mm & 40mm----Center of the Seed of Life-6 petalled flower -22mm 30mm 40mm----Seed of life Sacred Geometry 35mm----Seed of life 27mm 33mm 45mm----Seed of Life filled 29mm----Cuboctahedral Flower 35mm----Seed of Life within Seed of Life 40mm 34mm ----3d Seed of Life 30mm----3D Seed of Life Pendant 20mm----Seed of Life Genesa Sphere 20mm and 30mm----Spherical Vector Equilibrium - Genesa sphere...

This is a beautiful set of the 5 Platonic Solids plus the equally if not more important Vector Equilibrium. Buckminster Fuller was the one who named the cuboctahedron the 'Vector Equilibrium' and recognised its nature as the perfect balance of contractive and expansive forces. It's vertexes show the natural way that spheres cluster, with 12 points equally distant from their neighbors and from the central point. It is the 3d equivalent of the hexagon, showing the same symmetry as the 6 circles surrounding a central circle as they do in the Flower of Life. Even though it is classified as...

The way 12 stars can be made to enclose space is quite enchanting. This figure is made simply by replacing the pentagonal faces of a dodecahedron with 5 pointed stars. It is really only the dodecahedral and icosahedral forms that lend themselves to this kind of 'stellation'. Geometers tell us that it is only in two three, and four dimensions that this phenomena of stellating the platonic forms occurs. Star forms are inherently dynamic and unstable. It is interesting to contemplate that (to put it perhaps too simply) beyond the fourth dimension there are no stars. This model will be...

The way 12 stars can be made to enclose space is quite enchanting. This figure is made simply by replacing the pentagonal faces of a dodecahedron with 5 pointed stars. It is really only the dodecahedral and icosahedral forms that lend themselves to this kind of 'stellation'. Geometers tell us that it is only in two three, and four dimensions that this phenomena of stellating the platonic forms occurs. Star forms are inherently dynamic and unstable. It is interesting to contemplate that (to put it perhaps too simply) beyond the fourth dimension there are no stars. This model will be...

NOTE: the materials images above are mixed up, but you can gage what they would look like from any of our other models materials. The way 12 stars can be made to enclose space is quite enchanting. This figure is made simply by replacing the pentagonal faces of a dodecahedron with 5 pointed stars. It is really only the dodecahedral and icosahedral forms that lend themselves to this kind of 'stellation'. Geometers tell us that it is only in two three, and four dimensions that this phenomena of stellating the platonic forms occurs. Star forms are inherently dynamic and unstable....

A study of the possible symmetries of space. This is an extension of my other models based on the cubeoctahedron. This one has the 3 more axes showing the full cubic and octahedral symmetries. The Cubeoctahedral in blue with the Octahedral green.

The StarTetrahedron is one of the most important Sacred Geometrical forms. The tetrahedron is the simplest of the 5 Platonic Solids, but it is not fully symmetrical. However when two of them are interpenetrating like this then they are fully balanced, and their outer vertexes form a cube whilst their inner vertexes form an octahedron. Thus In one form the StarTetrahedron contains the 3 core shapes that exist in all dimensions, the 'Simplex', the 'Cross' and the "Measure'. Understanding how this triad of forms continues through the dimensions can open a window to perceiving higher dimensional geometries. The StarTetrahedron was...

This is one of my studies in 3 dimensionalizing the tradition Metatron's Cube design. I particularly enjoy its atomic rings from a certain perspective, and the ease with which you can see the 12 directions from the center Here we have two sets of 12 points surrounding the centre. If each of these points were joined to every other point we would have an exact 3D analog of the 2D Metatron's Cube. By analogy then if the 2D form is to be known as Metatron's Cube, then this form must be one dimensiona higher and be known as Metatron's Hypercube...

This version of the hypercube has fairly thick lines giving it a more chunky look. The Hypercube is the 4 dimensional analog of the cube. For full info on it see the Wikipedia article here. This model is an unusual projection of the Hypercube that equally distorts all 8 of its cubes. All the lines the same length as they should be in a Platonic hyper solid or 'polytope'. It is my own invention from about 36 years ago when I first got into drawing 3D stereographic models. It is the equivalent of drawing a cube as a hexagon with...