Tetrahedral vs. Cube Symmetries
(Tetrahedron inscribed in cube)
The above figure graphically demonstrates that the symmetry group of the tetrahedron (
T
_{d}
) is a sub-group of the symmetry group of the cube (
O
_{h}
). That is, any rotation, reflection, etc., which takes the tetrahedron into itself necessarily takes the cube into itself, but
not
vice versa!
© 1999 R. J. Hauenstein