Trigonal trapezohedron

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Trigonal trapezohedron
Trigonal trapezohedron
Click on picture for large version.
Type trapezohedra
Coxeter diagram CDel node fh.pngCDel 2.pngCDel node fh.pngCDel 6.pngCDel node.png
CDel node fh.pngCDel 2.pngCDel node fh.pngCDel 3.pngCDel node fh.png
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 triangular antiprism.

Hexahedron.jpg
A trigonal trapezohedron with square faces is a cube.

Related polyhedra[edit]

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

Gyroelongated triangular bipyramid.png
Family of trapezohedra
2 3 4 5 6 7 8 9 10 11 12 ...
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 4.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 2x.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 6.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 3.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 8.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 4.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 1x.pngCDel 0x.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 5.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 1x.pngCDel 2x.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 6.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 1x.pngCDel 4.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 7.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 1x.pngCDel 6.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 8.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 2x.pngCDel 0x.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 10.pngCDel node fh.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 2x.pngCDel 4.pngCDel node.png
CDel node fh.pngCDel 2x.pngCDel node fh.pngCDel 12.pngCDel node fh.png
Digonal trapezohedron.png TrigonalTrapezohedron.svg Tetragonal trapezohedron.png Pentagonal trapezohedron.svg Hexagonal trapezohedron.png Octagonal trapezohedron.png Decagonal trapezohedron.png
As spherical polyhedra
Spherical digonal antiprism.png Spherical trigonal trapezohedron.png Spherical tetragonal trapezohedron.png Spherical pentagonal trapezohedron.png Spherical hexagonal trapezohedron.png Spherical heptagonal trapezohedron.png Spherical octagonal trapezohedron.png Spherical decagonal trapezohedron.png Spherical dodecagonal trapezohedron.png

See also[edit]

External links[edit]