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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.
Forms

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

Triangular truncated trapezohedron (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 icosahedron
Truncated hexagonal trapezohedron – 12 pentagons, 2 hexagons, dual gyroelongated hexagonal dipyramid
...
Truncated n-gonal trapezohedron – 2n pentagons, 2 n-gons, dual gyroelongated dipyramids

See also

Diminished trapezohedron

External links

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

vte

Convex polyhedra
Platonic solids (regular)

tetrahedron cube octahedron dodecahedron icosahedron

Archimedean solids
(semiregular or uniform)

truncated tetrahedron cuboctahedron truncated cube truncated octahedron rhombicuboctahedron truncated cuboctahedron snub cube icosidodecahedron truncated dodecahedron truncated icosahedron rhombicosidodecahedron truncated icosidodecahedron snub dodecahedron

Catalan solids
(duals of Archimedean)

triakis tetrahedron rhombic dodecahedron triakis octahedron tetrakis hexahedron deltoidal icositetrahedron disdyakis dodecahedron pentagonal icositetrahedron rhombic triacontahedron triakis icosahedron pentakis dodecahedron deltoidal hexecontahedron disdyakis triacontahedron pentagonal hexecontahedron

Dihedral regular

dihedron hosohedron

Dihedral uniform

prisms antiprisms

duals:

bipyramids trapezohedra

Dihedral others

pyramids truncated trapezohedra gyroelongated bipyramid cupola bicupola pyramidal frusta bifrustum rotunda birotunda prismatoid scutoid

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