Regular dodecahedron dodecahedron forms an icosidodecahedron. The regular dodecahedron has icosahedral symmetry I, Coxeter group [5,3], order 120, with an abstract group structure of "A" × "Z". When a regular dodecahedron is inscribed in a sphere, it occupies more of the sphere's volume (66.49%) than an icosahedron inscribed in the same sphere (60.54%). A regular dodecahedron with edge length 1 has more than three and a half times the volume of an icosahedron with the same length edges (7.663... compared with 2.181...), which ratio is approximately , or in exact terms: or . A regular dodecahedron has 12 faces and 20 vertices,
Tetrated dodecahedron Johnson solid, the four triangles corresponding to the face planes of a tetrahedron are always equilateral, while the pentagons and the other triangles only have reflection symmetry. The 12 pentagons and 16 triangles are colored in this net by their locations within the tetrahedral symmetry. Tetrated dodecahedron The tetrated dodecahedron is a near-miss Johnson solid. It was first discovered in 2002 by Alex Doskey. It was then independently rediscovered in 2003 and named by Robert Austin. It has 28 faces: twelve regular pentagons arranged in four panels of three pentagons each, four equilateral triangles (shown in blue), and six pairs