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Octagonal prism

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Uniform octagonal prism
Type Prismatic uniform polyhedron
Elements F = 10, E = 24, V = 16 (χ = 2)
Faces by sides 8{4}+2{8}
Schläfli symbol t{2,8} or {8}×{}
Wythoff symbol 2 8 | 2
2 2 4 |
Coxeter diagrams


Symmetry D8h, [8,2], (*822), order 32
Rotation group D8, [8,2]+, (822), order 16
References U76(f)
Dual Octagonal dipyramid
Properties convex, zonohedron

Vertex figure
4.4.8

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

Symmetry

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Name Ditetragonal prism Ditetragonal trapezoprism
Image
Symmetry D4h, [2,4], (*422) D4d, [2+,8], (2*4)
Construction tr{4,2} or t{4}×{}, s2{2,8},

Images

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

Use

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

In uniform honeycombs and 4-polytopes

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It is an element of three uniform honeycombs:

Truncated square prismatic honeycomb
Omnitruncated cubic honeycomb
Runcitruncated cubic honeycomb

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

Runcitruncated tesseract
Omnitruncated tesseract
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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. 2.4.4 3.4.4 4.4.4 5.4.4 6.4.4 7.4.4 8.4.4 9.4.4 10.4.4 11.4.4 12.4.4 ... ∞.4.4
Coxeter diagram ...
*n42 symmetry mutation of omnitruncated tilings: 4.8.2n
Symmetry
*n42
[n,4]
Spherical Euclidean Compact hyperbolic Paracomp.
*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

4.8.4

4.8.6

4.8.8

4.8.10

4.8.12

4.8.14

4.8.16

4.8.∞
Omnitruncated
duals

V4.8.4

V4.8.6

V4.8.8

V4.8.10

V4.8.12

V4.8.14

V4.8.16

V4.8.∞
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  • Weisstein, Eric W. "Octagonal prism". MathWorld.
  • Interactive model of an Octagonal Prism