Editing Dodecahedron (section)

==Other dodecahedra==
There are 6,384,634 topologically distinct ''convex'' dodecahedra, excluding mirror images—the number of vertices ranges from 8 to 20.<ref>[http://www.numericana.com/data/polycount.htm Counting polyhedra]. Numericana.com (2001-12-31). Retrieved on 2016-12-02.</ref> (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

Topologically distinct dodecahedra (excluding pentagonal and rhombic forms)
*Uniform polyhedra:
**[[Decagonal prism]] – 10 squares, 2 decagons, [[dihedral symmetry|D<sub>10h</sub>]] symmetry, order 40.
**[[Pentagonal antiprism]] – 10 equilateral triangles, 2 pentagons, [[dihedral symmetry|D<sub>5d</sub>]] symmetry, order 20
*[[Johnson solid]]s (regular faced):
**[[Pentagonal cupola]] – 5 triangles, 5 squares, 1 pentagon, 1 decagon, [[cyclic symmetry|C<sub>5v</sub>]] symmetry, order 10
**[[Snub disphenoid]] – 12 triangles, [[dihedral symmetry|D<sub>2d</sub>]], order 8
**[[Elongated square dipyramid]] – 8 triangles and 4 squares, [[dihedral symmetry|D<sub>4h</sub>]] symmetry, order 16
**[[Metabidiminished icosahedron]] – 10 triangles and 2 pentagons, [[cyclic symmetry|C<sub>2v</sub>]] symmetry, order 4
*Congruent irregular faced: ([[face-transitive]])
**[[Hexagonal bipyramid]] – 12 isosceles [[triangle]]s, dual of [[hexagonal prism]], [[dihedral symmetry|D<sub>6h</sub>]] symmetry, order 24
**[[Hexagonal trapezohedron]] – 12 [[kite (geometry)|kites]], dual of [[hexagonal antiprism]], [[dihedral symmetry|D<sub>6d</sub>]] symmetry, order 24
**[[Triakis tetrahedron]] – 12 isosceles triangles, dual of [[truncated tetrahedron]], [[tetrahedral symmetry|T<sub>d</sub>]] symmetry, order 24
*Other less regular faced:
**Hendecagonal [[pyramid (geometry)|pyramid]] – 11 isosceles triangles and 1 regular [[hendecagon]], [[cyclic symmetry|C<sub>11v</sub>]], order 11
**[[Trapezo-rhombic dodecahedron]] – 6 rhombi, 6 [[trapezoid]]s – dual of [[triangular orthobicupola]], [[dihedral symmetry|D<sub>3h</sub>]] symmetry, order 12
**[[Rhombo-hexagonal dodecahedron]] or ''elongated Dodecahedron'' – 8 rhombi and 4 equilateral [[hexagon]]s, [[dihedral symmetry|D<sub>4h</sub>]] symmetry, order 16
**[[Truncated trapezohedron|Truncated pentagonal trapezohedron]], [[dihedral symmetry|D<sub>5d</sub>]], order 20, topologically equivalent to regular dodecahedron