Truncated trapezohedron

Set of $n$ -gonal truncated trapezohedra
Set of n-gonal truncated trapezohedra
	Example: pentagonal truncated trapezohedron (regular dodecahedron)
Faces	2 n-sided polygons,; 2n pentagons
Edges	6n
Vertices	4n
Conway notation	t4dA4 ; t5dA5 ; t6dA6
Symmetry group	Dnd, [2+,2n], (2*n), order 4n
Rotation group	Dn, [2,n]+, (22n), order 2n
Dual polyhedron	gyroelongated bipyramids
Properties	convex

In geometry, 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.

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

gyroelongated dipyramids, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron

Forms

gyroelongated triangular dipyramid
gyroelongated square dipyramid
Truncated pentagonal trapezohedron or regular dodecahedron – 12 pentagonal faces, dual icosahedron
gyroelongated hexagonal dipyramid
...
Truncated n-gonal trapezohedron – 2n pentagons, 2 n-gons, dual
gyroelongated dipyramids

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

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