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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. 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, with specific proportions:
References
Truncated square trapezohedron Wikipedia(Text) CC BY-SA