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.

A rotating Dodecahedron. A twelve faced 3D object that’s sides are pentagons. Animated GIF image - 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

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.

# Sections

# See also