Polyhedron with seven faces with four equilateral triangles and three squares. The squares intersect each other, bisecting each other along their diagonals. It has twelve edges and six vertices. It is a Hemipolyhedron, a uniform star polyhedron whose some of faces pass through its center.

The surface area of a tetrahemihexahedron with edge length $a$ is given by the formula:

The volume of a tetrahemihexahedron with edge length $a$ is given by the formula: