Octagonal prism

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

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

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 v t e
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 v t e
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.∞

External links

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