Octagonal prism

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Uniform octagonal prism
Octagonal prism.png
Type Prismatic uniform polyhedron
Elements F = 10, E = 24, V = 16 (χ = 2)
Faces by sides8{4}+2{8}
Schläfli symbol t{2,8} or {8}×{}
Wythoff symbol 2 8 | 2
2 2 4 |
Coxeter diagrams CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 8.pngCDel node.png
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png
CDel node 1.pngCDel 2.pngCDel node h.pngCDel 8.pngCDel node h.png
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 8.pngCDel node 1.png
Symmetry D8h, [8,2], (*822), order 32
Rotation group D8, [8,2]+, (822), order 16
References U 76(f)
Dual Octagonal dipyramid
Properties convex, zonohedron
Octagonal prism vertfig.png
Vertex figure
4.4.8
3D model of a uniform octagonal prism Octagonal prism.stl
3D model of a uniform octagonal prism

In geometry, the octagonal prism is a prism comprising eight rectangular sides joining two regular octagon caps.

Contents

Symmetry

NameDitetragonal prismDitetragonal trapezoprism
Image Truncated square prism.png Cantic snub octagonal hosohedron.png
SymmetryD4h, [2,4], (*422)D4d, [2+,8], (2*4)
Constructiontr{4,2} or t{4}×{}, CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngs2{2,8}, CDel node h.pngCDel 2x.pngCDel node h.pngCDel 8.pngCDel node 1.png

Images

The octagonal prism can also be seen as a tiling on a sphere:

Spherical octagonal prism.svg

Use

In optics, octagonal prisms are used to generate flicker-free images in movie projectors.

In uniform honeycombs and 4-polytopes

It is an element of three uniform honeycombs:

Truncated square prismatic honeycomb
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
Omnitruncated cubic honeycomb
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
Runcitruncated cubic honeycomb
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
Truncated square prismatic honeycomb.png Omnitruncated cubic honeycomb.jpg Runcitruncated cubic honeycomb.jpg

It is also an element of two four-dimensional uniform 4-polytopes:

Runcitruncated tesseract
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Omnitruncated tesseract
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
4-cube t013.svg 4-cube t0123.svg
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
*n42 symmetry mutation of omnitruncated tilings: 4.8.2n
Symmetry
*n42
[n,4]
Spherical Euclidean Compact hyperbolicParacomp.
*242
[2,4]
*342
[3,4]
*442
[4,4]
*542
[5,4]
*642
[6,4]
*742
[7,4]
*842
[8,4]...
*42
[,4]
Omnitruncated
figure
Spherical octagonal prism2.svg
4.8.4
Uniform tiling 432-t012.png
4.8.6
Uniform tiling 44-t012.svg
4.8.8
H2-5-4-omnitruncated.svg
4.8.10
H2 tiling 246-7.png
4.8.12
H2 tiling 247-7.png
4.8.14
H2 tiling 248-7.png
4.8.16
H2 tiling 24i-7.png
4.8.
Omnitruncated
duals
Spherical octagonal bipyramid2.png
V4.8.4
Spherical disdyakis dodecahedron.svg
V4.8.6
1-uniform 2 dual.svg
V4.8.8
H2-5-4-kisrhombille.svg
V4.8.10
Hyperbolic domains 642.png
V4.8.12
Hyperbolic domains 742.png
V4.8.14
Hyperbolic domains 842.png
V4.8.16
H2checkers 24i.png
V4.8.