From Wikipedia, the free encyclopedia
Polyhedron with 10 faces
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/10_sided_die.svg/220px-10_sided_die.svg.png)
Wikimedia Commons has media related to Decahedra.
In geometry, a decahedron is a polyhedron with ten faces. There are 32300 topologically distinct decahedra,[1][2] and none are regular, so this name does not identify a specific type of polyhedron except for the number of faces.
Some decahedra have regular faces:
- Octagonal prism (uniform 8-prism)
- Square antiprism (uniform 4-antiprism)
- Square cupola (Johnson solid 4)
- Pentagonal bipyramid (Johnson solid 13, 5-bipyramid)
- Augmented pentagonal prism (Johnson solid 52)
The decahedra with irregular faces include:
- Pentagonal trapezohedron (5-trapezohedron, antiprism dual) – often used as a die in role playing games, known as a d10
- Truncated square trapezohedron
- Enneagonal pyramid (9-pyramid)
- Ten of diamonds decahedron - a space-filling polyhedron with D2d symmetry.
References
[edit]- ^ Gerard Michon: Counting Polyhedra
- ^ Sloane, N. J. A. (ed.). "Sequence A000944". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
External links
[edit]Listed by number of faces and type | |
1–10 faces | |
11–20 faces | |
>20 faces |
|
elemental things |
|
convex polyhedron |
|
non-convex polyhedron |
|
prismatoids |
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url