Tetragonal antiwedge

The tetragonal antiwedge or tetaw is a polyhedron that consists of 4 scalene triangles and 2 irregular tetragons as faces, and is self-dual. It is the only chiral hexahedron under maximal symmetry and is one of two self-dual hexahedra, the other being the pentagonal pyramid.

Bi-tridiminished icosahedron
The bi-tridiminished icosahedron is a special case derived by diminishing 2 sets of 3 vertices from a regular icosahedron and is part of a family of diminished icosahedra, which includes the tridiminished icosahedron and the dodecahedron. It has 1+2+2 edges of length $$1$$ and 1+2+2 edges of length $$\frac{1+\sqrt5}2 \approx 1.61803$$. It occurs as the vertex figure of the bi-icositetradiminished hexacosichoron.