Set of truncated trapezohedra
Faces	2 n-gon Polygon In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments... s, 2n pentagon Pentagon In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and... s
Edges	6n
Vertices	4n
Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...	Dnd, [2+,2n], (2*n)
Dual polyhedron Dual polyhedron In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...	gyroelongated dipyramids
Properties	convex

An n-agonal truncated trapezohedron is a polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 formed by a n-agonal trapezohedron

Trapezohedron

The n-gonal trapezohedron, antidipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. Its 2n faces are congruent kites . The faces are symmetrically staggered.The n-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry...

 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

Platonic solid

In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

, 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

Icosahedron

In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....

 is the dual of the dodecahedron.

Forms

• Triangular truncated trapezohedron - 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid
• Square truncated trapezohedron
  Square truncated trapezohedron
  The square truncated trapezohedron is the second in an infinite series of truncated trapezohedron polyhedra. It has 8 pentagon and 2 square faces.This polyhedron can be constructed by taking a tetragonal trapezohedron and truncating the polar axis vertices....
  
   - 8 pentagons, 2 squares, dual gyroelongated square dipyramid
  Gyroelongated square dipyramid
  In geometry, the gyroelongated square bipyramid is one of the Johnson solids . As the name suggests, it can be constructed by gyroelongating an octahedron by inserting a square antiprism between its congruent halves...
  
  
• Pentagonal truncated trapezohedron or regular dodecahedron - 12 pentagonal faces, dual icosahedron
  Icosahedron
  In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
  
  
• Hexagonal truncated trapezohedron
  Hexagonal truncated trapezohedron
  The hexagonal truncated trapezohedron is the fourth in an infinite series of truncated trapezohedron polyhedra. It has 12 pentagon and 2 hexagon faces....
  
   - 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid
• ...
• n-agonal truncated trapezohedron - 2n pentagons, 2 n-agons, dual gyroelongated dipyramids

External links

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