Truncated trapezohedron
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| Set of truncated trapezohedra | |
|---|---|
| Image:Pentagonal truncated trapezohedron.png | |
| Faces | 2 n-gons, 2n pentagons |
| Edges | 6n |
| Vertices | 4n |
| Symmetry group | Dnd |
| Dual polyhedron | gyroelongated dipyramids |
| Properties | convex |
An n-agonal truncated trapezohedron is a polyhedron formed by a n-agonal trapezohedron with n-agonal pyramids truncated from its two polar axis vertices.
The vertices exist as 4 n-agons in four parallel planes, with alternating orientation in the middle creating the pentagons.
The regular dodecahedron is the most common polyhedron in this class, being a platonic solid, and 12 congruent pentagonal faces.
A truncated trapezohedron is interesting for having all vertices with 3 faces. This means that the dual polyhedra, se of gyroelongated dipyramid, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron.
[edit] Forms
Image:Square truncated trapezohedron.png Image:Pentagonal truncated trapezohedron.png Image:Hexagonal truncated trapezohedron.png
- Triangular truncated trapezohedron - 6 pentagons, 2 hexagons, dual gyroelongated triangular dipyramid
- Square truncated trapezohedron - 8 pentagons, 2 hexagons, dual gyroelongated square dipyramid
- Pentagonal truncated trapezohedron or regular dodecahedron - 12 pentagonal faces, dual icosahedron
- Hexagonal truncated trapezohedron - 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid
- ...
- n-agonal truncated trapezohedron - 2n pentagons, 2 n-agons, dual gyroelongated dipyramids
[edit] External link
- Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.
