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High Quality Content by WIKIPEDIA articles! An n-agonal truncated trapezohedron is a polyhedron formed by a n-agonal trapezohedron with n-agonal pyramids truncated from its two polar axis vertices. 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.