- These five remarkable solids - tetrahedron, cube, octahedron, dodecahedron, icosahedron - have faces that are congruent equilateral polygons.
- A dodecahedron modified by the octahedron and cube from Nordmark, Sweden, is figured in Goldschmidt.
- There is the octahedron, with 8 faces, 12 edges and 6 vertices.
- Plato believed that atoms have the shapes of regular polyhedra: cubes, tetrahedrons, octahedrons, and so on.
- Peterson and Jordan go on to investigate interesting links between integer octahedra and integer antiprisms.
- It was a set of platonic bodies: there was an octahedron and a double tetrahedron.
- Theaetetus was the first to study the octahedron and the icosahedron and it is believed that Book XIII of Euclid's Elements is based on his work.
- These are often known as the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron.
- Finally, the octahedron inscribed in the Venus-orbit sphere has itself an inscribed sphere, on which the orbit of Mercury lies.
- The cube, consisting of six square faces, is a common form either alone or in combination with other forms, especially the octahedron.
- I'd like to mention in passing that the octahedron, the dual of the cube, also contains 26: 8 faces, 12 edges, 6 vertices.
- This six-point perspective, with the six vertices of an octahedron serving as the vanishing points, becomes the basis of his spherical paintings.