Decahedron
Polyhedron with 10 faces
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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
- ^ Gerard Michon: Counting Polyhedra
- ^ Sloane, N. J. A. (ed.). "Sequence A000944". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
External links
- Weisstein, Eric W. "Decahedron". MathWorld.
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Listed by number of faces and type
- Icositetrahedron (24)
- Triacontahedron (30)
- Icosidodecahedron (32)
- Hexoctahedron (48)
- Hexecontahedron (60)
- Enneacontahedron (90)
- Hectotriadiohedron (132)
- Apeirohedron (∞)
- face
- edge
- vertex
- uniform polyhedron (two infinite groups and 75)
- regular polyhedron (9)
- quasiregular polyhedron (16)
- semiregular polyhedron (two infinite groups and 50)
- Platonic solid (5)
- Archimedean solid (13)
- Catalan solid (13)
- Johnson solid (92)
- Kepler–Poinsot polyhedron (4)
- Star polyhedron (infinite)
- Uniform star polyhedron (57)
- prism
- antiprism
- frustum
- cupola
- wedge
- pyramid
- parallelepiped
