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There are seven topologically different types of convex hexahedra and three concave ones. These have different names such as parallelepiped, left-handed tetragonal antiwedge, or simply "4,4,4,4,3,3 faces". The last of these is a tetrahedron with a v-shaped chunk cut out of one edge.

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Q: What can a hexahedron also be called?
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