The group of rotations of the four-dimensional hypercube and its action on the vertices of the hypercube - Kum, Romdoh; Felix, Rene P. (Quezon City 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.
Thesis (Master of Science in Mathematics)--University of the Philippines Diliman
Keywords: Mathematics; Hypercube