I've seen them in Bowers' dice page, and I've played with them in 4D toys, but I haven't found any precise description of how they're built.

I think I have an idea, though. Since gyrochora exist with any amount (n ≥ 5) of cells, I figured that their symmetry group must be (in general) cyclic. So I then thought that perhaps, an (m,n)-gyrochoron could be the dual of the convex hull of the action of a point under a double rotation of angles 2π/m and 2π/n. This would also explain why gyrochora don't exist for m or n equal to 1 (all points would lie on a two-dimensional plane).

Am I correct?