Truncated hexagonal trapezohedron

{{Short description|Truncated trapezohedron with a 6-sided base}}

{{Infobox polyhedron

| image = Hexagonal truncated trapezohedron.png

| euler =

| type = Truncated trapezohedron

| faces = 12 pentagons
2 hexagons

| edges = 36

| vertices = 24

| vertex_config =

| schläfli =

| wythoff =

| coxeter =

| conway = [https://levskaya.github.io/polyhedronisme/?recipe=C100t6dA6 t6dA6]

| symmetry = {{math|Symmetry_group#Three_dimensions, [12,2{{sup|+}}], 2*6,}} order 24

| rotation_group = {{math|D{{sub|6}}, [6,2]{{sup|+}}, 226,}} order 12

| surface_area =

| volume =

| dual = Gyroelongated hexagonal dipyramid

| properties = convex

| vertex_figure =

| net =

}}

In geometry, the truncated hexagonal trapezohedron is the fourth in an infinite series of truncated trapezohedra. It has 12 pentagon and 2 hexagon faces. It can be constructed by taking a hexagonal trapezohedron and truncating the polar axis vertices.

Weaire–Phelan structure

The Weaire–Phelan structure contains another form of this polyhedron that has D2d symmetry and is a part of a space-filling honeycomb along with an irregular dodecahedron.

class="wikitable"
align=center

|160px
Irregular tetradecahedron
(Truncated hexagonal trapezohedron)

|160px
Weaire–Phelan honeycomb

See also