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 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.

Forms

• 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

External links

• Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.