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
Type	Truncated trapezohedron Johnson solid dual
Faces	8 pentagons, 2 squares
Edges	24
Vertices	16
Symmetry group	D4d, [2+,8], (2*4)
Dual polyhedron	Gyroelongated square bipyramid (J17)
Properties	convex

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 polyhedron, the 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