41. Note the duality between the cube and the octahedron , and between the dodecahedron and the icosahedron. 42. For example, diamonds, which have a cubic crystal system, are often found as octahedrons . 43. Both names reflect the fact that it has three triangular faces for every face of an octahedron . 44. The lattice has two basic structure units the B 12 icosahedron and the B 6 octahedron . 45. The truncated octahedron is a bitruncated cube : 2t { 4, 3 } is an example. 46. Geometrically these points correspond to the vertices of a regular octahedron when aligned with the Cartesian axes. 47. The octahedron -first orthographic projection of the octahedral prism into 3D space has an octahedral envelope. 48. An octahedron has 12 edges, so the number would have to be a multiple of 12. 49. Thus it is a stellation of the octahedron , and in fact, the only finite stellation thereof. 50. Some interesting fold-out nets of the cube, octahedron , dodecahedron and icosahedron are available here.
