Truncated trapezohedron

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Set of truncated trapezohedra
Regular dodecahedron
Conway polyhedron notation t4dA4 t5dA5 t6dA6
Faces 2 n-gons,
2n pentagons
Edges 6n
Vertices 4n
Symmetry group Dnd, [2+,2n], (2*n), order 4n
Rotation group Dn, [2,n]+, (22n), order 2n
Dual polyhedron gyroelongated dipyramids
Properties convex

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.[citation needed]

The vertices exist as 4 n-gons 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, with 12 congruent pentagonal faces.

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.png Square truncated trapezohedron.png Pentagonal truncated trapezohedron.png Hexagonal truncated trapezohedron.png

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