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 | D_{8h}, [8,2], (*822), order 32 |
Rotation group | D_{8}, [8,2]^{+}, (822), order 16 |
References | U_{76(f)} |
Dual | Octagonal dipyramid |
Properties | convex, zonohedron |
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
Name | Ditetragonal prism | Ditetragonal trapezoprism |
---|---|---|
Image | ||
Symmetry | D_{4h}, [2,4], (*422) | D_{4d}, [2^{+},8], (2*4) |
Construction | tr{4,2} or t{4}×{}, | s_{2}{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
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.∞ |