# Dodecahedron

In geometry, a __dodecahedron__ (Greek ''hédra'' "base", "seat" or "face") is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three Kepler–Poinsot polyhedron, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. Platonic solid representing one of the four Classical element, the dodecahedron representing the universe The page of Harmonices Mundi from which these images are taken - wikimedia  Platonic solid representing one of the four Classical element, the dodecahedron representing the universe The page of Harmonices Mundi from which these images are taken - wikimedia Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular:

The #Pyritohedron, a common crystal form in pyrite, has pyritohedral symmetry, while the #Tetartoid has tetrahedral symmetry.

The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling polyhedra. There are numerous #Other dodecahedra.

While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner.

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