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. ... For other uses, see Square. ... Coxeter groups in the plane with equivalent diagrams. ... Image File history File links CDW_ring. ... Image File history File links No higher resolution available. ... 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. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... A polyhedron (plural polyhedra or polyhedrons) 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. ... This article or section is not written in the formal tone expected of an encyclopedia article. ... 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). ... The infinity symbol ∞ in several typefaces. ...

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 right 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 (now usually pronounced , traditionally[1] in accordance with its etymology in Greek παραλληλ-επίπεδον, a body having parallel planes) is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ... This article or section is not written in the formal tone expected of an encyclopedia article. ...

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. ...

An equilateral square prism is simply a cube. A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ...

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, or the height (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. ...

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...

See also

• Prismatic uniform polyhedron.
• Cylinder (geometry)

A prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. ... 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). ...

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