The group of rotations of the four-dimensional hypercube and its action on the vertices of the hypercube - Kum, Romdoh (College of Science, University of the Philippines Diliman, 2015)
The four-dimensional hypercube has 192 rotations which send the hypercube to itself. We study the group G consisting of these 192 rotations and look at its action on the set of V of 16 vertices of the hypercube. The subgroup structure of G was determined. In particular, subgroups of G of order 8, 12, 16, 24 were studied and their isomorphism determined. Colorings from two types of subgroup S of order 16 were investigated. If S acts transitively on V, left coset coloring of V were considered and it was checked if they correspond to symmetric colorings. The second type was a subgroup S where V is partitioned into two S-orbits. Here, a single set of colors was used to color V. The effect of retaining the colors in one orbit and permuting the assignment of colors in the secnd orbit was studied.