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

Faces	2n triangle Triangle A triangle is one of the basic shape [i]s of geometry [i]: a polygon [i] with three vertices [i] ... s
Edges	3n
Vertices	n+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] ...	D_nh 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
Properties	convex, 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
...

D_nh.

Forms

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

A cube is a three-dimensional [i] Platonic solid [i] composed of six square [i] ...
Pentagonal bipyramid - 10 faces - dual pentagonal prism
Hexagonal bipyramid - 12 faces - dual hexagonal prism
Heptagonal bipyramid - 14 faces - dual heptagonal prism
Octagonal bipyramid - 16 faces - dual octagonal prism
Enneagonal bipyramid - 18 faces - dual enneagonal prism
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 ...

D_nh 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 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 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.