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Did you mean: Trihemic Hexahedron

Tetrahemihexahedron

In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U₄. It has 7 faces, 12 edges, and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is. The tetrahemihexahedron... Wikipedia
Dual polyhedron: Tetrahemihexacron
Faces by sides: 4+3
Wythoff symbol: 3/2 3 | 2 (double-covering)