Truncated square trapezohedron

In geometry, the square truncated trapezohedron is the second in an infinite series of truncated trapezohedra. It has 8 pentagon and 2 square faces.

Truncated square trapezohedron
TypeTruncated trapezohedron
Johnson solid dual
Faces8 pentagons,
2 squares
Edges24
Vertices16
Symmetry groupD4d, [2+,8], (2*4)
Dual polyhedronGyroelongated square bipyramid (J17)
Propertiesconvex

This polyhedron can be constructed by taking a tetragonal trapezohedron and truncating the polar axis vertices. The kite faces of the trapezohedron become pentagons.

The vertices exist as 4 squares in four parallel planes, with alternating orientation in the middle creating the pentagons.

A truncated trapezohedron has all valence-3 vertices. This means that the dual polyhedrona gyroelongated square dipyramid has all triangular faces.

It represents the dual polyhedron to the Johnson solid, gyroelongated square dipyramid (J17), with specific proportions:

Square truncated trapezohedron Net