Truncated square trapezohedron
{{Short description|Truncated trapezohedron with a 4-sided base}}
{{Infobox polyhedron
| image = Square truncated trapezohedron.png
| euler =
| type = Truncated trapezohedron
Johnson solid dual
| faces = 8 pentagons,
2 squares
| edges = 24
| vertices = 16
| vertex_config =
| schläfli =
| wythoff =
| coxeter =
| conway =
| symmetry = {{math|Symmetry_group#Three_dimensions, [2{{sup|+}},8], (2*4)}}
| rotation_group =
| surface_area =
| volume =
| dual = Gyroelongated square bipyramid ({{math|J{{sub|17}}}})
| properties = convex
| vertex_figure =
| net =
}}
In geometry, the square truncated trapezohedron is the second in an infinite series of truncated trapezohedra. 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 polyhedron, the gyroelongated square dipyramid, has all triangular faces.
It represents the dual polyhedron to the Johnson solid, gyroelongated square dipyramid ({{math|J{{sub|17}}}}), with specific proportions:
| class=wikitable width=320 |
| valign=top
!Square truncated trapezohedron !Net |
| valign=top |
{{Polyhedron-stub}}