Set of uniform prisms
Type	uniform polyhedron
Faces	2 p-gons, p squares
Edges	3p
Vertices	2p
Coxeter-Dynkin diagram
Vertex configuration	4.4.p
Symmetry group	Dph
Dual polyhedron	bipyramids
Properties	convex, semi-regular vertex-transitive

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids. Image File history File links Hexagonal_prism. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... Look up polygon in Wiktionary, the free dictionary. ... In plane (Euclidean) geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides. ... Coxeter groups in the plane with equivalent diagrams. ... Image File history File links CDW_ring. ... Image File history File links CDW_dot. ... Image File history File links CDW_2. ... Image File history File links CDW_ring. ... In polyhedral geometry a vertex configuration is a short-hand notation for representing a vertex as the sequence of faces around a vertex. ... The symmetry group of an object (e. ... The symmetry group of an object (e. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... A bipyramid is a polyhedron formed by joining two identical pyramids base-to-base. ... In mathematics, a vertex-transitive graph is a graph G such that, given any two vertices v1 and v2 of G, there is some automorphism f : G → G such that f ( v1 ) = v2. ... Table of Geometry, from the 1728 Cyclopaedia. ... A polyhedron is a geometric object with flat faces and straight edges. ... Look up polygon in Wiktionary, the free dictionary. ... In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. ... A parallelogram. ... A prismatoid is a polyhedron where all vertices lie in two parallel planes. ...

General, right and uniform prisms

A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining faces are rectangular.

In the case of a rectangular or square prism there may be ambiguity because some texts may mean a right rectangular-sided prism and a right square-sided prism.

The term uniform prism can be used for a right prism with square sides since such prisms are in the set of uniform polyhedra. A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...

An n-prism, made of regular polygons ends and rectangle sides approaches a cylindrical solid as n approaches infinity. A regular pentagon A regular polygon is a simple polygon (a polygon which does not intersect itself anywhere) which is equiangular (all angles are equal) and equilateral (all sides have the same length). ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... This article or section is not written in the formal tone expected of an encyclopedia article. ...

Right prisms with regular bases and equal edge lengths form one of the two infinite series of semiregular polyhedra, the other series being the antiprisms. A semiregular polyhedron is a geometric shape constructed from a finite number of regular polygon faces with every face edge shared by one other face, and with every vertex containing the same sequence of faces, and, moreover, for every two vertices there is an isometry mapping one into the other. ... An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles. ...

The dual of a uniform prism is a bipyramid. In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... A bipyramid is a polyhedron formed by joining two identical pyramids base-to-base. ...

A parallelepiped is a prism of which the base is a parallelogram, or equivalently a polyhedron with 6 faces which are all parallelograms. In geometry, a parallelepiped (pronounced ; meaning of parallel planes) or parallelopipedon is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ... A parallelogram. ...

A right rectangular prism is also called a cuboid, or informally a rectangular box. A right square prism is simply a square box, and may also be called a square cuboid. In anatomy, the cuboid bone is a bone in the foot. ...

Uniform prisms

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.N...

Image File history File links Triangular_prism. ... In geometry, a triangular prism or three-sided prism is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. ... Image File history File links Download high-resolution version (1000x1000, 201 KB)Image of Cube, colored with dihedral symmetry Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... Image File history File links Pentagonal_prism. ... In geometry, the pentagonal prism is the third in an infinite set of prisms formed by square sides and two regular polygon caps. ... Image File history File links Hexagonal_prism. ... In geometry, the hexagonal prism is the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. ... Image File history File links Octagonal_prism. ... In geometry, the octagonal prism is the sixth in an infinite set of prisms formed by square sides and two regular polygon caps. ... Image File history File links Download high-resolution version (1000x1000, 154 KB)Decagonal prism Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In geometry, the decagonal prism is the eighth in an infinite set of prisms formed by square sides and two regular polygon caps. ... Image File history File links Download high-resolution version (1000x1000, 159 KB)Dodecagonal prism Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In geometry, the dodecagonal prism is the tenth in an infinite set of prisms formed by square sides and two regular polygon caps. ...

Area and volume

The volume of a prism is the product of the area of the base and the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... Area is a physical quantity expressing the size of a part of a surface. ...

Symmetry

The symmetry group of a right n-sided prism with regular base is D_nh of order 4n, except in the case of a cube, which has the larger symmetry group O_h of order 48, which has three versions of D_4h as subgroups. The rotation group is D_n of order 2n, except in the case of a cube, which has the larger symmetry group O of order 24, which has three versions of D₄ as subgroups. The symmetry group of an object (e. ... This article may be confusing for some readers, and should be edited to enhance clarity. ... The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ... In mechanics and geometry, the rotation group is the set of all rotations about the origin of 3-dimensional Euclidean space, R3. ...

The symmetry group contains inversion iff n is even. In Euclidean geometry, the inversion of a point X in respect to a point P is a point X* such that P is the midpoint of the line segment with endpoints X and X*. In other words, the vector from X to P is the same as the vector from... IFF, Iff or iff can stand for: Interchange File Format - a computer file format introduced by Electronic Arts Identification, friend or foe - a radio based identification system utilizing transponders iff - the mathematics concept if and only if International Flavors and Fragrances - a company producing flavors and fragrances International Freedom Foundation...

Star prisms

There are also uniform prisms that can be constructed by star polygons: {n/m} = {5/2}, {7/3}, {7/4}, {8/3}, {9/2}, {9/4}, {10/3}... In geometry, a star polygon is a complex, equilateral equiangular polygon, so named for its starlike appearance, created by connecting one vertex of a simple, regular, n-sided polygon to another, non-adjacent vertex and continuing the process until the original vertex is reached again. ...

{5/2}

{7/2}

{7/3}

{8/3}

{9/2}

Image File history File links Pentagrammic_prism. ... In geometry, the pentagrammic prism is the first in an infinite set of concave prisms formed by square sides and two regular star polygon caps, in this case two pentagrams. ... Image File history File links Download high resolution version (1000x1000, 279 KB) Licensing Robert Webb produced this image for Wikipedia upon my request, and offered the credit statement below: File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In geometry, the {7/2} heptagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two {7/2} heptagrams. ... Image File history File links Download high-resolution version (1000x1000, 276 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Alternative representation with hollow heptagram centers In geometry, the {7/3} heptagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two {7/3} heptagrams. ...

See also

• Uniform_polyhedron#Dihedral_symmetry.
• Michelob; a "Michelob Golden" can is a regular thirty-sided prism.

A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... Michelob is the trade name of a family of beers produced by the Anheuser-Busch brewery. ...

External links

• Eric W. Weisstein, Prism at MathWorld.
• Olshevsky, George, Prismatic polytope at Glossary for Hyperspace.
• Nonconvex Prisms and Antiprisms
• Surface Area MATHguide
• Volume MATHguide
• Paper models of prisms and antiprisms Free nets of prisms and antiprisms
• Paper models of prisms and antiprisms
• Prisms (Cross Section Illustration)
• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra
  • VRML models (George Hart) <3> <4> <5> <6> <7> <8> <9> <10>