Octagonal prism

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

Uniform octagonal prism
TypePrismatic uniform polyhedron
ElementsF = 10, E = 24, V = 16 (χ = 2)
Faces by sides8{4}+2{8}
Schläfli symbolt{2,8} or {8}×{}
Wythoff symbol2
2 2 4 |
Coxeter diagrams


SymmetryD8h, [8,2], (*822), order 32
Rotation groupD8, [8,2]+, (822), order 16
ReferencesU76(f)
DualOctagonal dipyramid
Propertiesconvex, zonohedron

Vertex figure
4.4.8

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

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