Dodecahedron - Other Dodecahedra

Other Dodecahedra

The term dodecahedron is also used for other polyhedra with twelve faces, most notably the rhombic dodecahedron which is dual to the cuboctahedron (an Archimedean solid) and occurs in nature as a crystal form. The Platonic solid dodecahedron can be called a pentagonal dodecahedron or a regular dodecahedron to distinguish it. The pyritohedron is an irregular pentagonal dodecahedron.

Topologically distinct dodecahedra include:

• Pentagonal dodecahedra:
  • Regular dodecahedron, 12 pentagonal faces, I_h symmetry, order 120
  • Pentagonal truncated trapezohedron - same topology as regular form, but D_5d symmetry, order 20
  • "Pyritohedron" - same topology as regular form, but T_h symmetry, order 12
• Uniform polyhedra:
  • Decagonal prism – 10 squares, 2 decagons, D_10h symmetry, order 40
  • Pentagonal antiprism – 10 equilateral triangles, 2 pentagons, D_5d symmetry, order 20
• Johnson solids (regular faced):
  • Pentagonal cupola – 5 triangles, 5 squares, 1 pentagon, 1 decagon, C_5v symmetry, order 10
  • Snub disphenoid – 12 triangles, D_2d, order 8
  • Elongated square dipyramid – 8 triangles and 4 squares, D_4h symmetry, order 16
  • Metabidiminished icosahedron – 10 triangles and 2 pentagons, C_2v symmetry, order 4
• Congruent nonregular faced: (face-transitive)
  • Hexagonal bipyramid – 12 isosceles triangles, dual of hexagonal prism, D_6h symmetry, order 24
  • Hexagonal trapezohedron – 12 kites, dual of hexagonal antiprism, D_6d symmetry, order 24
  • Triakis tetrahedron – 12 isosceles triangles, dual of truncated tetrahedron, T_d symmetry, order 24
  • Rhombic dodecahedron (mentioned above) – 12 rhombi, dual of cuboctahedron, O_h symmetry, order 48
• Other nonregular faced:
  • Hendecagonal pyramid – 11 isosceles triangles and 1 hendecagon, C_11v, order 11
  • Trapezo-rhombic dodecahedron – 6 rhombi, 6 trapezoids – dual of triangular orthobicupola, D_3h symmetry, order 12
  • Rhombo-hexagonal dodecahedron or Elongated Dodecahedron – 8 rhombi and 4 equilateral hexagons, D_4h symmetry, order 16

In all there are 6,384,634 topologically distinct dodecahedra.