Dodecagonal prism

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Uniform dodecagonal prism
Dodecagonal prism.png
Type Prismatic uniform polyhedron
Elements F = 14, E = 36, V = 24 (χ = 2)
Faces by sides12{4}+2{12}
Schläfli symbol t{2,12} or {12}×{}
Wythoff symbol 2 12 | 2
2 2 6 |
Coxeter diagrams CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 12.pngCDel node.png
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.png
CDel node 1.pngCDel 2.pngCDel node h.pngCDel 12.pngCDel node h.png
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 12.pngCDel node 1.png
Symmetry D12h, [12,2], (*12.2.2), order 48
Rotation group D12, [12,2]+, (12.2.2), order 24
References U 76(j)
Dual Dodecagonal dipyramid
Properties convex, zonohedron
Dodecagonal prism vf.png
Vertex figure
4.4.12
3D model of a uniform dodecagonal prism Dodecagonal prism.stl
3D model of a uniform dodecagonal prism

In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.

Contents

If faces are all regular, it is a uniform polyhedron.

Use

It is used in the construction of two prismatic uniform honeycombs:

Omnitruncated triangular-hexagonal prismatic honeycomb.png
Omnitruncated triangular-hexagonal prismatic honeycomb
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
Truncated hexagonal prismatic honeycomb.png
Truncated hexagonal prismatic honeycomb
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png

The new British one pound (£1) coin, which entered circulation in March 2017, is shaped like a dodecagonal prism. [1]

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 Yellow square.gif Triangular prism.png Tetragonal prism.png Pentagonal prism.png Hexagonal prism.png Prism 7.png Octagonal prism.png Prism 9.png Decagonal prism.png Hendecagonal prism.png Dodecagonal prism.png ...
Spherical tiling image Spherical digonal prism.svg Spherical triangular prism.svg Spherical square prism.svg Spherical pentagonal prism.svg Spherical hexagonal prism.svg Spherical heptagonal prism.svg Spherical octagonal prism.svg Spherical decagonal prism.svg Plane tiling image Infinite prism.svg
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 CDel node 1.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 8.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 9.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 10.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 11.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel node 1.pngCDel 12.pngCDel node.pngCDel 2.pngCDel node 1.png...CDel node 1.pngCDel infin.pngCDel node.pngCDel 2.pngCDel node 1.png

References

  1. "New 12-sided pound coin to enter circulation in March". BBC News. 2017-01-01. Retrieved 2017-04-20.