¶ Allspace Filling
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Index Entry
Allspace Filling:
“The tetrahedron will not fill all space. If we take an equilateral triangle and bisect its edges and put three little tetrahedra on the three corners of the triangle and put a fourth tetrahedron in the center, we find that there is not enough room for other mm tetrahedra to come down in the crevices between the peaks of the tetrahedra. So you cannot fill all space with tetrahedra. What you do is fill all space with tetrahedra and octahedra. They complement one another. But if you were looking for a monological explanation this wouldn’t be nice for you. If you are willing to go along with the physicists, recognizing complementarity, then you would say that this method of accounting, which is coming out nice and rational, is a perfectly good way of accounting. I could talk tetrahedra even though I am using different forms. Now we have tetrahedra being agglomerated with octahedra and we have a very interesting kind of condition.”
¶ Citations
- OREGON Lecture #6, p. 216, 10 Jul’62, incorporated in SYNERGETICS at Secs. 950.01 (Gray) + 950.34 (Gray) 14 Nov’72
