[math-fun] genus-1 polytopes in 4-space

I was thinking about genus-1 polytopes in 4-space, and I was wondering if some of them would be considered "regular". For example, the cartesian product of two identical regular polygons is a two-dimensional surface (like the surface of a torus), which can be distorted to fit in 3-space but which is much more symmetrical in 4-space. As a specific example, here's a torus surface in 4-space whose cross sections are squares: max(|w|, |x|) = 1 max(|y|, |z|) = 1 Unless I'm mistaken, all of its faces are squares (16 of them, the cartesian products of the edges of the squares), and it is face-transitive, edge-transitive, and vertex-transitive. Does that make it regular? Tom