Truncated square trapezohedron

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Square truncated trapezohedron
Square truncated trapezohedron.png
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 dipyramid
Properties convex

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:

Square truncated trapezohedron Net
Dual gyroelongated square dipyramid.png Dual gyroelongated square dipyramid net.png