See Also

Bipyramid

An n-agonal bipyramid or dipyramid is a polyhedron Polyhedron

A polyhedron is a geometric shape which in mathematics [i] is defined by three related meanings. ... 

 formed by joining an n-agonal pyramid Pyramid

Pyramids are among the largest man-made constructions as well as one of the great Wonders of the ancient world... 

 and its mirror image base-to-base. The referenced n-agon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves. The face-uniform bipyramids are the dual polyhedra Dual polyhedron

In geometry [i], polyhedra [i] are associated into pairs called duals, where the vertices [i] ... 

 of the uniform prisms and will generally have isosceles triangle Triangle

A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... 

 faces. Three bipyramids can be made out of all equilateral triangle Triangle

A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... 

s, the octahedron Octahedron

An octahedron is a polyhedron [i] with eight faces. ... 

 , which counts among the Platonic solid Platonic solid

In geometry [i], a Platonic solid is a convex [i] regular polyhedron [i]. ... 

s, and the triangular and pentagonal bipyramids, which count among the Johnson solid Johnson solid

In geometry [i], a Johnson solid is a convex [i] polyhedron [i], each face of which is a regular polygon [i] ... 

s.

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Encyclopedia

Set of bipyramids

Faces2n triangle Triangle

A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... 

s
Edges3n
Verticesn+2
Face configuration Face configuration

In geometry, a face configuration is notational description of a face-uniform [i] polyhedron [i]. ... 

V4.4.n
Symmetry group Symmetry group

The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ... 

Dnh Symmetry group

The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ... 

Dual polyhedron Dual polyhedron

In geometry [i], polyhedra [i] are associated into pairs called duals, where the vertices [i] ... 

Prisms
Propertiesconvex, face-uniform





An n-agonal bipyramid or dipyramid is a polyhedron Polyhedron

A polyhedron is a geometric shape which in mathematics [i] is defined by three related meanings. ... 

 formed by joining an n-agonal pyramid Pyramid

Pyramids are among the largest man-made constructions as well as one of the great Wonders of the ancient world... 

 and its mirror image base-to-base.

The referenced n-agon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves.

The face-uniform bipyramids are the dual polyhedra Dual polyhedron

In geometry [i], polyhedra [i] are associated into pairs called duals, where the vertices [i] ... 

 of the uniform prisms and will generally have isosceles triangle Triangle

A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... 

 faces.

Three bipyramids can be made out of all equilateral triangle Triangle

A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... 

s, the octahedron Octahedron

An octahedron is a polyhedron [i] with eight faces. ... 

 , which counts among the Platonic solid Platonic solid

In geometry [i], a Platonic solid is a convex [i] regular polyhedron [i]. ... 

s, and the triangular and pentagonal bipyramids, which count among the Johnson solid Johnson solid

In geometry [i], a Johnson solid is a convex [i] polyhedron [i], each face of which is a regular polygon [i] ... 

s.

A bipyramid can be projected Perspective projection

Perspective projection is a type of drawing [i], or rendering, that graphically approximates on a planar ... 

 on a sphere or globe Globe

This article is on a planet-representation device.... 

 as n equally spaced lines of longitude going from pole to pole, and bisected Bisection

[i]
[i]
... 

 by a line around the equator Equator

The equator is an imaginary circle [i] drawn around a planet [i] at a distance halfway between the pole [i] ... 

.

Bipyramid face Face

The face is the front part of the head [i], in humans [i] from the forehead to chin including the ... 

s, projected as spherical triangle Spherical trigonometry

[i]s on the [[sphere]... 

s, represent the fundamental domains in the dihedral symmetry List of spherical symmetry groups

List of symmetry group [i]s on the sphere
... 

 Dnh.

Forms

  1. Triangular bipyramid - 6 faces - dual triangular prism
  2. Tetragonal bipyramid - 8 faces - dual cube Cube

    A cube is a three-dimensional [i] Platonic solid [i] composed of six square [i] ... 

  3. Pentagonal bipyramid - 10 faces - dual pentagonal prism
  4. Hexagonal bipyramid - 12 faces - dual hexagonal prism
  5. Heptagonal bipyramid - 14 faces - dual heptagonal prism
  6. Octagonal bipyramid - 16 faces - dual octagonal prism
  7. Enneagonal bipyramid - 18 faces - dual enneagonal prism
  8. Decagonal bipyramid - 20 faces - dual decagonal prism

  • ...n-agonal bipyramid - 2n faces - dual n-agonal prism

Symmetry groups

If the base is regular and the line through the apexes intersects the base at its center, the symmetry group List of spherical symmetry groups

List of symmetry group [i]s on the sphere
... 

 of the n-agonal bipyramid has dihedral symmetry Dihedral group

In mathematics [i], the dihedral group of order [i] 2n is the abstract group of which one repr ... 

 Dnh of order 4n, except in the case of a regular octahedron, which has the larger octahedral symmetry Octahedral symmetry

A regular octahedron [i] has 24 rotational symmetries, and a total of 48 symmetries including transformations ... 

 group Oh of order 48, which has three versions of D4h as subgroups.
The rotation group is Dn of order 2n, except in the case of a regular octahedron, which has the larger symmetry group O of order 24, which has three versions of D4 as subgroups.

External links

  • The Encyclopedia of Polyhedra
    • VRML models
      • Try: "dPn", where n=3,4,5,6... example "dP4" is an octahedron.