Uniform Triangular prism
Type	Semiregular polyhedron
Elements	F=5, E=9, V=6 (χ=2)
Faces by sides	3{4}+2{3}
Schläfli symbol	t{2,3}
Wythoff symbol	2 3 | 2
Coxeter-Dynkin
Symmetry	D3h
References	U76(a)
Dual	Triangular dipyramid
Properties	convex
Vertex figure 4.4.3

In geometry, a triangular prism or three-sided prism is a type of prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. Image File history File links Triangular_prism. ... 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. ... It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ... In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ... In geometry, a Wythoff construction, named after mathematician Willem Abraham Wijthoff, is a method for constructing a uniform polyhedron or plane tiling. ... Coxeter groups in the plane with equivalent diagrams. ... Image File history File links CDW_ring. ... Image File history File links CDW_3. ... Image File history File links CDW_dot. ... Image File history File links CDW_2. ... Image File history File links CDW_ring. ... // List of symmetry groups on the sphere Spherical symmetry groups are also called point groups (in 3D). ... This article deals with three infinite series of point groups in three dimensions which have a symmetry group which as abstract group is a dihedral group Dihn ( n ≥ 2 ). See also point groups in two dimensions. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... In geometry, the triangular dipyramid is a polyhedron made entirely out of 6 faces, which are all equilateral triangles, 9 edges, and 5 vertexes. ... Look up Convex set in Wiktionary, the free dictionary. ... Image File history File links Triangular_prism_vertfig. ... In polyhedral geometry a vertex configuration is a short-hand notation for representing a vertex as the sequence of faces around a vertex. ... Diagram of a triangular prism, dispersing light Lamps as seen through a prism. ... 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. ... 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. ... A polyhedron (plural polyhedra or polyhedrons) is a geometric object with flat faces and straight edges. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. ...

If the sides are squares, it is called a uniform polyhedron. In general the sides can be congruent rectangles. A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...

Equivalently, it is a pentahedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes). These three faces are parallelograms. All cross-sections parallel to the base faces are the same triangle. In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ... A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ... This article or section is not written in the formal tone expected of an encyclopedia article. ...

A right triangular prism is semiregular if the base faces are equilateral triangles, and the other three faces are squares. 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. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... For other uses, see Square. ...

A general right triangular prism can have rectangular sides.

The dual of a triangular prism is a 3-sided 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. ...

The symmetry group of a right 3-sided prism with regular base is D_3h of order 12. The rotation group is D₃ of order 6. The symmetry group of an object (e. ... This article may be confusing for some readers, and should be edited to enhance clarity. ... 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 does not contain inversion. 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...

Volume

The volume of any prism is the product of the area of the base and the distance between the two base faces. In this case the base is a triangle so we simply need to compute the area of the triangle and multiply this by the length of the prism. A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ...

See also

• Prism (geometry)
• Semiregular E-polytope family:
  • triangular prism: -1₂₁
  • rectified 5-cell: 0₂₁
  • demipenteract: 1₂₁
  • E6 polytope: 2₂₁
  • E7 polytope: 3₂₁
  • E8 polytope: 4₂₁
  • E8 lattice: 5₂₁

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. ... In geometry, the Rectified 5-cell is a polychoron composed of 5 regular tetrahedra and 5 regular octahedra cells. ... A demipenteract is a name for a semiregular 5-polytope, constructed from a penteract with alternated vertices deleted. ... In mathematics, the E6 polytope is the convex hull of the roots of E6. ... In mathematics, E7 is the name of several Lie groups and also their Lie algebras . ... In mathematics, E8 is the name given to a family of closely related structures. ... In mathematics, the E8 lattice is a special lattice in R8. ...

External links

• Eric W. Weisstein, Triangular prism at MathWorld.
• Paper model triangular prism Prism nets