A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals).It is represented by the Schläfli symbol. Properties The dihedral angle of a regular dodecahedron is 2 arctan(ϕ) or approximately 116.565° the golden ratio). OEIS: A137218 Note that the tangent of the dihedral angle is exactly −2. If the original regular dodecahedron has edge length 1, its dual icosahedron has edge length ϕ. If the five Platonic solids are built with same volume, the regular dodecahedron has the shortest edges. It has 43,380 nets. The map-coloring number of a regular dodecahedron's faces is 4. The distance between the vertices on the same face not connected by an edge is ϕ times the edge length. If two edges share a common vertex, then the midpoints of those edges form a 36-72-72 triangle with the body center.

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