¶ Prime Structural Systems
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Index Entry
There are three types of omnitriangular, symmetrical structural systems. We can have three triangles around each vertex; a tetrahedron. Or we can have four triangles around each vertex; the octahedron. Finally we can have five triangles around each vertex; the icosahedron.
The tetrahedron, octahedron, and icosahedron are made up, respectively, of one, two, and five pairs of positively and negatively functioning open triangles.
We cannot have six symmetrical or equiangural triangles around each vertex because the angles add up to 360 degrees–thus forming an infinite edgeless plane. The system with six equiangular triangles ‘flat out’ around each vertex never comes back upon itself. It can have no withinness or withoutness. It cannot be constructed with pairs of positively and negatively functioning open triangles. In order to have a system, it must return upon itself in all directions.
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