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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.

Q: What is another name for hexahedron?

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A polygon is a 2-dimensional shape whereas a hexahedron is 3-dimensional. Therefore a polygon that is a hexahedron could by called a geometric impossibility.

A hexahedron.