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

|160px

|160px

Category:Polyhedra

{{Polyhedron-stub}}