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catenary and a tetrahedron
Posted:
Aug 10, 2013 10:42 AM


WHICH TETRAHEDRONS FILL SPACE
Debates about filling space with tet. are very old, and going on even today. I either don?t fully understand the question, or everybody on the subject than must be wrong.
I understand that the reg. plat. tetrahedron does not fill space by it?s self, but we know it can fill space with a another vol. identical. tet. which is derived from a reg. plat. non space filling octahedron.
So in this arrangement a reg. tet. and a 1/4 octahedron fill space. What I visualize here is that when ever one combine these pieces if he builds a unit octet. truss, or a reg. rhombic hexahedron, or a hexagonal squashed prism, or a cubeoctahedron or any symmetry any pattern possible, all what happens in this case, is that our tet. octa. structure is just a small fraction of the infinitely large tetrahedron, we just seeing the fraction of the whole, as ever larger and large space is filled the final product is a infinitely LARGE REG. PLATONIC TETRAHEDRON that contains all the inner structures.
Now my point is, no matter how one arranges these pieces, these pieces or units, or what ever they resemble, they are always just a small portion of the larger whole, since every tetrahedron contains a inner octahedron, so the whole final product will be a tetrahedron.
And this result is true no MATTER what kind of tet. is involved. I see it like a catenary curve. If one see a catenary curve, in a suspension bridge, or electric power lines, or just a hanging chain, even though all these curves look different but all they are just a single catenary curve, observed from a different portion of the curve.
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