¶ Octahedron (1)
← Octahedron: Volume of Cube as Three (3) | Octahedron (2) →
Index Entry
“Here we take an octahedron which has a volume of four. An octahedron has six vertexes and it is symmetrical because they are all equilateral triangles and all the edges are the same. Therefore we know by it being symmetrical that if we interconnect its opposite vertexes, being six of them, there will be three axes between the six opposite vertexes. Those three axes would be the well-known XYZ coordinate system and the XYZ coordinates then do exist inside the octahedron. If I cut the octahedron through one of the four planes, one of the planes of its equator, it makes me two half-octahedra. If the volume of an octahedron in respect to a tetrahedron is four, then a half-octahedron has a volume of two, and 2 + 2 = 4.”
¶ Citations
- Oregon Lecture #6, p.214. 10 Jul’62
