Tetrahedroning (2)

← Tetrahedroning (1) | Tetrahedroning (3) →

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 (C): 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"