This geometric figure has SchlÃ¤fli symbol {4, 3}, and its symmetry group has order 48.
This geometric figure has SchlÃ¤fli symbol {4, 3}, and its symmetry group has order 48. It is a zonohedron with 3 generators, and rotating it about an axis through its two furthest points gives a hyperboloid of one sheet. Menaechmus solved a problem involving the duplication of this figure, which is impossible with only a compass and straightedge. This figure's dual is the octahedron, and its longest space diagonal is root-three times its side length. With a dihedral angle of 90 degrees, it is the Platonic solid with the second-smallest number of faces and the only one that can tile space. For 10 points, name this regular polyhedron with six square faces.
This geometric figure has SchlÃ¤fli symbol {4, 3}, and its symmetry group has order 48.
cube or regular hexahedron 