# Dodecahedron

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Regular Dodecahedron

(Click here for rotating model)
Type Platonic solid
Elements F = 12, E = 30
V = 20 (χ = 2)
Faces bi sides 12{5}
Schläfli seembols {5,3}
Wythoff seembol 3 | 2 5
Coxeter diagram
Symmetry Ih, H3, [5,3], (*532)
Rotation group I, [5,3]+, (532)
References U23, C26, W5
Properties Regular convex
Dihedral angle 116.56505° = arccos(-1/√5)

5.5.5
(Vertex figure)

Icosahedron
(dual polyhedron)

Net

In geometry, a dodecahedron (Greek δωδεκάεδρον, frae δώδεκα, dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is ony polyhedron wi twelve flat faces, but uisually a regular dodecahedron is meant: a Platonic solid. It is componed o 12 regular pentagonal faces, wi three meetin at each vertex, an is representit bi the Schläfli seembol {5,3}. It haes 20 vertices, 30 edges an 160 diagonals. Its dual polyhedron is the icosahedron, wi Schläfli seembol {3,5}.

A lairge nummer o ither (irregular) polyhedra an aa hae twelve faces, maist notably the topologically identical pyritohedron wi Pyritohedral symmetry, an the rhombic dodecahedron wi octahedral symmetry.