The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of
the corresponding tetragonal trapezohedron are

The skeleton of the tetragonal trapezohedron is a non-cubic graph (it has degree sequence (3, 3, 3, 3, 3,
3, 3, 3, 4, 4)) in which all faces touch an even number of sides but the graph is
not three-colorable.