¶ Tetrahedroning (2)
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Index Entry
Tetrahedroning:
"Here is one tetrahedron (A). Here I have three tetrahedra and one octahedron (B). This is the plateau of an equilateral triangle. It is a truncated tetrahedron. If I take the sum of the volumes here, three tetrahedra plus four for the octahedron, the volume is seven.
"I am now going to make the next level of equilateral triangles ©: we add a row of three tetrahedra and we add two octahedra between them. We must also add an upside-down tetrahedron to go in the middle between the octahedra. The accounting is now six tetrahedra and each tetra has a volume of one; three octahedra and each octa has a volume of four (3 x 4 = 12). So 6 + 12 = 18, plus one inverted tetrahedron = 19, which is the volume of this group. It has a truncated top which is a 2-module triangle.
“Here is the next bigger triangle (D) with a row of four additional tetrahedra, three additional octahedra, and two additional upside-down tetrahedra to go between the two new octahedra. The accounting of this aggregation is 10 tetrahedra”
