Dodecahedron

Common dodecahedra<table><tbody><tr><th colspan="4">Ih, order 120</th></tr><tr><td><a href="/facts/Regular_dodecahedron/xClYqhcp">Regular</a></td><td><a href="/facts/Small_stellated_dodecahedron/lX1zlo6C">Small stellated</a></td><td><a href="/facts/Great_dodecahedron/LWt3Hgg4">Great</a></td><td><a href="/facts/Great_stellated_dodecahedron/7efrgSub">Great stellated</a></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><th>Th, order 24</th><th>T, order 12</th><th>Oh, order 48</th><th>Johnson (J84)</th></tr><tr><td><a href="/facts/Pyritohedron/7r519eCl">Pyritohedron</a></td><td><a href="/facts/Tetartoid/7r519eCl">Tetartoid</a></td><td><a href="/facts/Rhombic_dodecahedron/X3npAlmr">Rhombic</a></td><td><a href="/facts/Triangular_dodecahedron/kdLUzB07">Triangular</a></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><th colspan="2">D4h, order 16</th><th colspan="2">D3h, order 12</th></tr><tr><td><a href="/facts/Rhombo-hexagonal_dodecahedron/IARRN28r">Rhombo-hexagonal</a></td><td><a href="/facts/Rhombic_dodecahedron/X3npAlmr">Rhombo-square</a></td><td><a href="/facts/Trapezo-rhombic_dodecahedron/CNSrcoWh">Trapezo-rhombic</a></td><td><a href="/facts/Triangular-rhombic_dodecahedron/CNSrcoWh">Rhombo-triangular</a></td></tr><tr><td></td><td></td><td></td><td></td></tr></tbody></table>
In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a dodecahedron (from <a href="/facts/Ancient_Greek_language/LIK7NlUh">Ancient Greek</a> δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron is any <a href="/facts/Polyhedron/UC0p9FTF">polyhedron</a> with twelve flat faces. The most familiar dodecahedron is the <a href="/facts/Regular_dodecahedron/xClYqhcp">regular dodecahedron</a> with regular pentagons as faces, which is a <a href="/facts/Platonic_solid/jraREXFD">Platonic solid</a>. There are also three <a href="/facts/Kepler%25E2%2580%2593Poinsot_polyhedron/mzUUgBYS">regular star dodecahedra</a>, which are constructed as <a href="/facts/Stellation/T7NY6CWv">stellations</a> of the convex form. All of these have <a href="/facts/Icosahedral_symmetry/pDlwAy23">icosahedral symmetry</a>, 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 <a href="/facts/Pyrite/41CYREyr">pyrite</a>, has <a href="/facts/Pyritohedral_symmetry/hIVlf9pu">pyritohedral symmetry</a>, while the tetartoid has <a href="/facts/Tetrahedral_symmetry/hIVlf9pu">tetrahedral symmetry</a>.
The <a href="/facts/Rhombic_dodecahedron/X3npAlmr">rhombic dodecahedron</a> can be seen as a limiting case of the pyritohedron, and it has <a href="/facts/Octahedral_symmetry/qLqhYxgm">octahedral symmetry</a>. The <a href="/facts/Elongated_dodecahedron/IARRN28r">elongated dodecahedron</a> and <a href="/facts/Trapezo-rhombic_dodecahedron/CNSrcoWh">trapezo-rhombic dodecahedron</a> variations, along with the rhombic dodecahedra, are <a href="/facts/Space-filling_polyhedra/seyRBcel">space-filling</a>. 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.

Dodecahedron open-in-new

Dodecahedron