← Module: B Module | one-eighth octahedron →
Index Entry
Module: B Module:
*Pogonics:
"The one-quarter tetrahedron and the one-eighth octahedron each have an equilateral triangular base and each of the (base ?) edges are identical in length. We can superimpose the one-eighth octahedron over the one-quarter tetrahedron because the volume of the one-eighth octahedron is one half and the volume of the one-quarter tetrahedron is one quarter, so the volume of the one-eighth octahedron is twice that of the one-quarter tetrahedron. Therefore, they will have the same base and the one-eighth octahedron must have twice the altitude because it has the same base and its volume is twice as great.
"In figure #25 they are superimposed and there is a space between the surface of the one-eighth octahedron and the surface of the one-quarter tetrahedron because the one-eight octahedron has a volume twice that of the one-quarter tetrahedron, the space between the two must be the same as the one-quarter tetrahedron so this space in here is a unit of one and the one-quarter tetrahedron is a volume of one. That is, the space between is superimposed as a concave lid and it has a volume of one. If you would actually make that a solid and weigh them, they would have the same weight.
