|Set of truncated trapezohedra|
|Dual polyhedron||gyroelongated dipyramids|
The vertices exist as 4 n-agons 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 dipyramid, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron.
- Triangular truncated trapezohedron - 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid
- Square truncated trapezohedron - 8 pentagons, 2 squares, 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
- Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.
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