Trigonal trapezohedron

Trigonal trapezohedron
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Type	trapezohedra
Coxeter diagram
Faces	6 rhombi
Edges	12
Vertices	8
Face configuration	3,3,3,3
Symmetry group	D3d, [2+,6], (2*3), order 12
Rotation group	D3, [2,6]+, (223), order 6
Dual polyhedron	trigonal antiprism
Properties	convex, face-transitive

In geometry, a trigonal trapezohedron or trigonal deltohedron is a three-dimensional figure formed by six congruent rhombi. They are a special kind of parallelepiped, and are the only parallelepipeds with six congruent faces. Since all of the edges must have the same length, every trigonal trapezohedron is also a rhombohedron.

The trigonal trapezohedron is the simplest of the trapezohedra, an infinite sequence of polyhedra which are dual to the antiprisms. The dual of a trigonal trapezohedron is a uniform triangular antiprism, i.e. a regular octahedron.

A trigonal trapohederon with square faces is a cube.

Related polyhedra

An octahedron augumented by 2 tetrahedron creates a trigonal trapezohedron, with coplanar triangles merged into 60 degree rhombic faces.

Family of trapezohedra

2	3	4	5	6	7	8	9	10	11	12	...
As spherical polyhedra

See also

• Truncated triangular trapezohedron

External links

• Weisstein, Eric W., "Trapezohedron", MathWorld.