Heptahedron

Also notable is the tetrahemihexahedron, which can be seen as a tessellation of the real projective plane.

There are 34 topologically distinct convex heptahedra, excluding mirror images.

[2] (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

Six topologically distinct concave heptahedra (excluding mirror images) can be formed by combining two tetrahedra in various configurations.

[citation needed] 13 topologically distinct heptahedra (excluding mirror images) can be formed by cutting notches out of the edges of a triangular prism or square pyramid.

A diminished cube , realized with 4 equilateral-triangle and 3 kite faces, all having the same area, [ 1 ]
The Szilassi polyhedron