Dodecahedron
Polyhedron with 12 faces / From Wikipedia, the free encyclopedia
In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron[1] 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 regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
Ih, order 120 | |||
---|---|---|---|
Regular- | Small stellated- | Great- | Great stellated- |
Th, order 24 | T, order 12 | Oh, order 48 | Johnson (J84) |
Pyritohedron | Tetartoid | Rhombic- | Triangular- |
D4h, order 16 | D3h, order 12 | ||
Rhombo-hexagonal- | Rhombo-square- | Trapezo-rhombic- | Rhombo-triangular- |
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. 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.[2]