610.20 Omnitriangular Symmetry: Three Prime Structural Systems

610.21 There are only three types of fundamental, omnitriangular, symmetrical structural systems. We can have three triangles around each vertex of a symmetrical structure; this makes a regular tetrahedron. Or we can have four triangles around each vertex; this makes the regular octahedron. Finally we can have five triangles around each vertex; this makes the icosahedron.

610.22 The tetrahedron, octahedron, and icosahedron are made up, respectively, of one, two, and five pairs of positively and negatively functioning open triangles.

610.23 We cannot have six symmetrical or equiangular triangles around each vertex because the angles add up to 360 degreesthus 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.

610.24 Limit Cases: Macro, Medio, and Micro: Considered geometrically, triangles are the only self-stabilizing polygonal patternsergo, only triangles are structurally stable. Since we cannot construct a polyhedral system of only two triangles around each corner (because a polyhedral system must by definition have an insideness and an outsideness in order definitively and closingly to separate the Universe into macrocosm and microcosm), and since we cannot have six equilateral triangles around each vertex of a polyhedral system (for each of the six would themselves separate out from the others to form flat planes and could not close back to join one another to separate Universe definitively into macrocosm and microcosm)ergo, the tetrahedron, octahedron, and icosahedron constitute the minimum, middle, and maximum cases of omnitriangulatedergo, stabilized structural subdividings of Universe into macro, medio, and micro Universe divisions.