Octagonal prism

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Uniform Octagonal prism
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}x{}
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 2.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 U76(f)
Dual Octagonal dipyramid
Properties convex, zonohedron
Octagonal prism
Vertex figure
4.4.8

In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.

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

Symmetry[edit]

Image Truncated square prism.png Cantic snub octagonal hosohedron.png
Symmetry D4h, [2,4], (*422) D4d, [2+,8], (2*4)
Constructiopn tr{4,2} or t{4}×{}, CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png s2{2,8}, CDel node h.pngCDel 2.pngCDel node h.pngCDel 8.pngCDel node 1.png

Images[edit]

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

Spherical octagonal prism.png

Use[edit]

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

In uniform honeycombs and polychora[edit]

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 polychora:

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

Related polyhedra[edit]

Family of uniform prisms
Symmetry 3 4 5 6 7 8 9 10 11 12
[2n,2]
[n,2]
[2n,2+]
CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 6.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 8.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 8.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 9.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 10.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 10.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 11.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 12.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 12.pngCDel node h.pngCDel 2.pngCDel node h.png
Image Triangular prism.png Tetragonal prism.png
Uniform polyhedron 222-t012.png
Cube rotorotational symmetry.png
Pentagonal prism.png Hexagonal prism.png
Truncated triangle prism.png
Cantic snub hexagonal hosohedron.png
Prism 7.png Octagonal prism.png
Truncated square prism.png
Cantic snub octagonal hosohedron.png
Prism 9.png Decagonal prism.png Hendecagonal prism.png Dodecagonal prism.png
As spherical polyhedra
Image Spherical triangular prism.png Spherical square prism.png
Spherical square prism2.png
Spherical pentagonal prism.png Spherical hexagonal prism.png
Spherical hexagonal prism2.png
Spherical heptagonal prism.png Spherical octagonal prism.png
Spherical octagonal prism2.png
Spherical decagonal prism.png
Spherical decagonal prism2.png
Dimensional family of omnitruncated polyhedra and tilings: 4.8.2n
Symmetry
*n42
[n,4]
Spherical Euclidean Compact hyperbolic Paracompact
*242
[2,4]
D4h
*342
[3,4]
Oh
*442
[4,4]
P4m
*542
[5,4]
*642
[6,4]
*742
[7,4]
*842
[8,4]...
*∞42
[∞,4]
Omnitruncated
figure
Spherical octagonal prism2.png
4.8.4
Uniform tiling 432-t012.png
4.8.6
Uniform tiling 44-t012.png
4.8.8
H2 tiling 245-7.png
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.∞
Coxeter
Schläfli
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{2,4}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{3,4}
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{4,4}
CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{5,4}
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{6,4}
CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{7,4}
CDel node 1.pngCDel 8.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{8,4}
CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 4.pngCDel node 1.png
tr{∞,4}
Omnitruncated
duals
Hexagonale bipiramide.png
V4.8.4
Disdyakisdodecahedron.jpg
V4.8.6
Tiling Dual Semiregular V4-8-8 Tetrakis Square.svg
V4.8.8
Order-4 bisected pentagonal tiling.png
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.∞
Coxeter CDel node f1.pngCDel 2.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 4.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 5.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 6.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 8.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel infin.pngCDel node f1.pngCDel 4.pngCDel node f1.png

External links[edit]