The Truncated Truncated Tetrahedron

twice truncated tet

This is the result, if one performs a second truncation to the truncated tetrahedron, in such as a way as to make the resulting dodecagons regular. To do this, however, regularity of the triangles and hexagons must be sacrificed — they are merely isosceles and equiangular, respectively.

[Image made using Stella 4d, software available here.]