Decagonal prism

In geometry, the decagonal prism is the eighth in the infinite set of prisms, formed by ten square side faces and two regular decagon caps. With twelve faces, it is one of many nonregular dodecahedra. The decagonal prism has 12 faces, 30 edges, and 20 vertices, so, it is a dodecahedron (while the term is usually applied to regular dodecahedron or rhombic dodecahedron.). If faces are all regular, it is a semiregular or prismatic uniform polyhedron.

Uniform decagonal prism
TypePrismatic uniform polyhedron
ElementsF = 12, E = 30, V = 20 (χ = 2)
Faces by sides10{4}+2{10}
Schläfli symbolt{2,10} or {10}×{}
Wythoff symbol2 10 | 2
2 2 5 |
Coxeter diagrams


SymmetryD10h, [10,2], (*10.2.2), order 40
Rotation groupD10, [10,2]+, (10.2.2), order 20
ReferencesU76(h)
DualDecagonal dipyramid
Propertiesconvex, zonohedron

Vertex figure
4.4.10

Uses

The decagonal prism exists as cells in two four-dimensional uniform 4-polytopes:

Runcitruncated 120-cell
Omnitruncated 120-cell

Decagonal prisms are often used in combination locks.

Family of uniform n-gonal prisms
Prism name Digonal prism (Trigonal)
Triangular prism
(Tetragonal)
Square prism
Pentagonal prism Hexagonal prism Heptagonal prism Octagonal prism Enneagonal prism Decagonal prism Hendecagonal prism Dodecagonal prism ... Apeirogonal prism
Polyhedron image ...
Spherical tiling image Plane tiling image
Vertex config. 2.4.43.4.44.4.45.4.46.4.47.4.48.4.49.4.410.4.411.4.412.4.4...∞.4.4
Coxeter diagram ...
  • Weisstein, Eric W. "Prism". MathWorld.
  • 3-d model of a Decagonal Prism
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