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Topologically equivalent forms A topological rhombic dodecahedron can be seen inside of a hexagonal prism, with hexagons dissected into rhombi in complementary ways between top and bottom. These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with a square pyramid attached to each face, and that the six square pyramids could fit together to a cube of the same size, i.e the rhombic dodecahedron has twice the volume of the inscribed cube with edges equal to the short diagonals of the rhombi. The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (☑, ☑, ☑) and (0, 1 + h, 1 − h 2) with parameter h = 1. The coordinates of the six vertices where four faces meet at their acute angles are: Pyritohedron variations between a cube and rhombic dodecahedronįor edge length √3, the eight vertices where three faces meet at their obtuse angles have Cartesian coordinates: The last two correspond to the B 2 and A 2 Coxeter planes. The rhombic dodecahedron has four special orthogonal projections along its axes of symmetry, centered on a face, an edge, and the two types of vertex, threefold and fourfold. R i = 6 3 a ≈ 0.8 a Orthogonal projections
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