In geometry, an truncated trapezohedron is a polyhedron formed by a trapezohedron with pyramids truncated from its two polar axis vertices. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism. The vertices exist as 4 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 In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

is the dual of the dodecahedron.

Forms

Triangular truncated trapezohedron In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedra. It has 6 pentagon and 2 triangle faces. Geometry This polyhedron can be constructed by truncating two opposite vertices of a cub ...

( Dürer's solid) – 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid * Truncated square trapezohedron – 8 pentagons, 2 squares, dual gyroelongated square dipyramid *''Truncated pentagonal trapezohedron'' or regular dodecahedron – 12 pentagonal faces, dual

* Truncated hexagonal trapezohedron – 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid *... *Truncated ''n''-gonal trapezohedron – 2''n'' pentagons, 2 ''n''-gons, dual gyroelongated dipyramids

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Conway Notation for Polyhedra
Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron. Polyhedra Truncated tilings {{polyhedron-stub

Forms

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