|Set of truncated trapezohedra|
|Symmetry group||Dnd, [2+,2n], (2*n), order 4n|
|Rotation group||Dn, [2,n]+, (22n), order 2n|
|Dual polyhedron||gyroelongated dipyramids|
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.
The vertices exist as 4 n-gons in four parallel planes, with alternating orientation in the middle creating the pentagons.
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.
- Triangular truncated trapezohedron (Dürer's solid) – 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid
- Truncated square trapezohedron – 8 pentagons, 2 squares, dual gyroelongated square dipyramid
- Truncated pentagonal trapezohedron or regular dodecahedron – 12 pentagonal faces, dual icosahedron
- Truncated hexagonal trapezohedron – 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid
- Truncated n-gonal trapezohedron – 2n pentagons, 2 n-gons, dual gyroelongated dipyramids
- Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.