This article is about the three-dimensional shape. It is not to be confused with Roman dodecahedron.
Common dodecahedra
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-
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.
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]
^1908 Chambers's Twentieth Century Dictionary of the English Language, 1913 Webster's Revised Unabridged Dictionary
^Athreya, Jayadev S.; Aulicino, David; Hooper, W. Patrick (May 27, 2020). "Platonic Solids and High Genus Covers of Lattice Surfaces". Experimental Mathematics. 31 (3): 847–877. arXiv:1811.04131. doi:10.1080/10586458.2020.1712564. S2CID 119318080.
In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve', and ἕδρα (hédra) 'base, seat, face') or duodecahedron...
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at...
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan...
A Roman dodecahedron or Gallo-Roman dodecahedron is a small hollow object made of copper alloy which has been cast into a regular dodecahedral shape: twelve...
In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of . It is one of four nonconvex...
a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron; that is, it...
a dodecahedron in other ways, they may result in an augmented dodecahedron (J58), a metabiaugmented dodecahedron (J60), a triaugmented dodecahedron (J61)...
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed...
In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5⁄2,3}. It is one of four nonconvex regular polyhedra...
In geometry, the augmented dodecahedron is one of the Johnson solids (J58), consisting of a dodecahedron with a pentagonal pyramid (J2) attached to one...
dodecahedron are dual to each other. The small stellated dodecahedron and great dodecahedron are dual to each other. The great stellated dodecahedron...
changing the orientation or size of the faces, or do the same to its dual dodecahedron, and patch the square holes in the result, you get a rhombicosidodecahedron...
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges...
In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (J60). It can be viewed as a dodecahedron with two pentagonal pyramids (J2)...
elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic...
faces meeting around each vertex. Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal faces around each vertex. The...
Platonic solids, there is no ball whose knobs match the 20 vertices of the dodecahedron, and the arrangement of the knobs was not always symmetric. The ancient...
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four...
dodecahedron in other ways, they may result in an augmented dodecahedron (J58), a parabiaugmented dodecahedron (J59), a metabiaugmented dodecahedron (J60)...
In geometry, the dyakis dodecahedron /ˈdʌɪəkɪsˌdəʊdɪkəˈhiːdrən/ or diploid is a variant of the deltoidal icositetrahedron with pyritohedral symmetry, transforming...
In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed...
pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect...
In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology but a different geometry...
octahedron Compound of small stellated dodecahedron and great dodecahedron Compound of great stellated dodecahedron and great icosahedron Wenninger, Magnus...
In geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. Its...
non-trivial stellations of the dodecahedron: Small stellated dodecahedron Great dodecahedron Great stellated dodecahedron This disambiguation page lists...
great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron...
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