Set of truncated trapezohedra | |
---|---|
Conway polyhedron notation | t4dA4 t5dA5 t6dA6 |
Faces | 2 n-gons, 2n pentagons |
Edges | 6n |
Vertices | 4n |
Symmetry group | D_{nd}, [2^{+},2n], (2*n), order 4n |
Rotation group | D_{n}, [2,n]^{+}, (22n), order 2n |
Dual polyhedron | gyroelongated dipyramids |
Properties | convex |
An n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis vertices. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism.^{[citation needed]}
The vertices exist as 4 n-gons 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, with 12 congruent pentagonal faces.
A truncated trapezohedron has all vertices with 3 faces. This means that the dual polyhedra, the set of gyroelongated dipyramids, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron.