Truncated trapezohedron

Truncated trapezohedron

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.

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

* [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron.

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