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