Rectified truncated tetrahedron

{{Short description|Convex polyhedron with 20 faces}}

{{Infobox polyhedron

| image = Rectified_truncated_tetrahedron.png

| type =

| faces = 20:
4 equilateral triangles
12 isosceles triangles
4 hexagons

| edges = 48

| vertices = 12+18

| vertex_config =

| schläfli = {{math|rt{3,3} }}

| wythoff =

| conway = {{math|atT}}

| coxeter =

| symmetry = {{math|T_d, [3,3], (*332),}} order 24

| rotation_group = {{math|T, [3,3]⁺, (332),}} order 12

| dual = Joined truncated tetrahedron

| properties = convex

| vertex_figure =

| net = Rectified truncated tetrahedron net.png

}}

In geometry, the rectified truncated tetrahedron is a polyhedron, constructed as a rectified, truncated tetrahedron. It has 20 faces: 4 equilateral triangles, 12 isosceles triangles, and 4 regular hexagons.

Topologically, the triangles corresponding to the tetrahedron's vertices are always equilateral, although the hexagons, while having equal edge lengths, do not have the same edge lengths with the equilateral triangles, having different but alternating angles, causing the other triangles to be isosceles instead.