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A dodecahedron is a regular polyhedron, one of the five three-dimensional platonic solids, and has twelve congruent pentagonal faces. It has a schläfli symbol of \{5, 3\}, meaning that 3 pentagons join at each vertex. It is the dual of the icosahedron.

Properties

It is possible to inscribe 5 cubes into a dodecahedron such that all of the edges of the cubes are diagonals of the dodecahedron's faces.

It is also the only platonic solid to have pentagonal faces.

Subfacets and Structure

Structure

The dodecahedron has 12 pentagonal faces, joining three to a vertex. When seen face first, the layers start with one face, then the five surrounding it, then five more, and finally the opposite face.

Hypervolumes

Subfacets

See Also

\{2,3\} \{3,3\} \{4,3\} \{5,3\} \{6,3\} \{7,3\} \{8,3\} ... \{\aleph_0,3\}
Trigonal hosohedron Tetrahedron Cube Dodecahedron Hexagonal tiling Order-3 heptagonal tiling Order-3 octagonal tiling ... Order-3 apeirogonal tiling
\{5,2\} \{5,3\} \{5,4\} \{5,5\} \{5,6\} ... \{5,\aleph_0\}
Pentagonal dihedron Dodecahedron Order-4 pentagonal tiling Order-5 pentagonal tiling Order-6 pentagonal tiling ... Infinite-order pentagonal tiling
Regular
t_0 \{5,3\}
Rectified
t_1 \{5,3\}
Birectified
t_2 \{5,3\}
Truncated
t_{0,1} \{5,3\}
Bitruncated
t_{1,2} \{5,3\}
Cantellated
t_{0,2} \{5,3\}
Cantitruncated
t_{0,1,2} \{5,3\}
Dodecahedron Icosidodecahedron Icosahedron Truncated dodecahedron Truncated icosahedron Rhombicosidodecahedron Great rhombicosidodecahedron

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