¶ Tetrahedroning (3)
← Tetrahedroning (2) | Tetrahedroning →
Index Entry
Tetrahedroning:
"with points up (10); plus six octahedra (6 x 4 = 24); plus three upside-down tetrahedra (3). So 10 + 24 + 3 = 37, which is the volume of this group.
"We are then going to superimpose the first tetrahedron and the truncated sections in sequence. We add (A) and (B) with a combined value of 8, to © 19 for a combined value of 27. We can do this because B8s module of two sits on a module-of-two base. Combining the whole stack with a base module of three, we can sit it on the base module of three of the plateau (D), resulting in a large tetrahedron whose edge module is four all the way through. The Volume of A-B-C was 27 and the D group was 37 for a combined volume of 64.
“So we discover that eight is the third power of module two; 27 is the third power of the module-three pyramid; and 64 is the volume of the module four. In other words, 8, 27, and 64 are simply the third powers of 2, 3, and 4. Therefore, instead of saying ‘cubing,’ we say tetrahedroning.”
¶ Citations
- Oregon Lecture #6, pp.217-218, 10 Jul’62
