The 24-cells are rotated with respect to each other in increments of . The rotational distance between inscribed 24-cells is always a double rotation of 0 to 4 increments of in one invariant plane, combined with 0 to 4 increments of in the orthogonal invariant plane, where the invariant planes are any two orthogonal central decagons. The product of these two 5-click simple rotations produces 25 distinct ways we can pick the 24 vertices of a 24-cell out of the 120 vertices of a 600-cell.