| 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 | 22 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 figure4.4.8 | |
In geometry, the octagonal prism is a prism comprising eight rectangular sides joining two regular octagon caps.
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Symmetry
| 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
The octagonal prism can also be seen as a tiling on a sphere:
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 | Omnitruncated cubic honeycomb | Runcitruncated cubic honeycomb |
It is also an element of two four-dimensional uniform 4-polytopes:
| Runcitruncated tesseract | Omnitruncated tesseract |
Related polyhedra
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] | |
| Omnitruncatedfigure | 4.8.4 | 4.8.6 | 4.8.8 | 4.8.10 | 4.8.12 | 4.8.14 | 4.8.16 | 4.8.∞ |
| Omnitruncatedduals | V4.8.4 | V4.8.6 | V4.8.8 | V4.8.10 | V4.8.12 | V4.8.14 | V4.8.16 | V4.8.∞ |