In geometry, 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.
|Set of n-gonal truncated trapezohedra|
|Faces||2 n-sided polygons,|
|Conway notation||t4dA4 |
|Symmetry group||Dnd, [2+,2n], (2*n), order 4n|
|Rotation group||Dn, [2,n]+, (22n), order 2n|
|Dual polyhedron||gyroelongated bipyramids|
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.