In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the octagonal prism is the sixth in an infinite set of prisms

Prism (geometry)

In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...

, formed by square sides and two regular octagon caps.

If faces are all regular, it is a semiregular polyhedron

Semiregular polyhedron

The term semiregular polyhedron is used variously by different authors.In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron...

.

Use

In optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, octagonal prisms are used to generate flicker-free images in movie projector

Movie projector

A movie projector is an opto-mechanical device for displaying moving pictures by projecting them on a projection screen. Most of the optical and mechanical elements, except for the illumination and sound devices, are present in movie cameras.-Physiology:...

s.

In uniform honeycombs and polychora

It is an element of three uniform honeycombs:

Truncated square prismatic honeycomb Truncated square prismatic honeycomb The truncated square prismatic honeycomb is a space-filling tessellation in Euclidean 3-space. It is composed of octagonal prisms and cubes in a ratio of 1:1.It is constructed from a truncated square tiling extruded into prisms....	Omnitruncated cubic honeycomb Omnitruncated cubic honeycomb The omnitruncated cubic honeycomb is a uniform space-filling tessellation in Euclidean 3-space. It is composed of truncated cuboctahedra and octagonal prisms in a ratio of 1:3.A wireframe rendering- References :...	Runcitruncated cubic honeycomb Runcitruncated cubic honeycomb The runcitruncated cubic honeycomb is a uniform space-filling tessellation in Euclidean 3-space. It is composed of small rhombicuboctahedra, truncated cubes, octagonal prisms, and cubes in a ratio of 1:1:3:3....

It is also an element of two four-dimensional uniform polychora

Uniform polychoron

In geometry, a uniform polychoron is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra....

:

Runcitruncated tesseract	Omnitruncated tesseract

See also

• Set of prisms
  Prism (geometry)
  In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...
  
  
• Triangular prism
  Triangular prism
  In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....
  
  
• Cube
  Cube
  In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
  
   (square-capped prism)
• Pentagonal prism
  Pentagonal prism
  In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.- As a semiregular polyhedron :...
  
  
• Hexagonal prism
  Hexagonal prism
  In geometry, the hexagonal prism is a prism with hexagonal base. The shape has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces...