Develops a geometric framework for understanding the 4-dimensional point groups through discrete Hopf fibrations and polar orbit polytopes, providing visual and structural insight into these symmetry groups.
Studies the dimension of the realization space of convex polytopes, establishing new bounds and results for families of polytopes with restricted combinatorial types.
Doctoral dissertation combining two lines of research: the geometry of 4-dimensional point groups via discrete Hopf fibrations, and the dimension theory of realization spaces of convex polytopes.
The number of finite subgroups of order n of the orthogonal group O(4). Sequence and accompanying table for n = 1..10000 computed as part of the research on 4-dimensional point groups.
The number of finite subgroups of order n of the special orthogonal group SO(4). Sequence and accompanying table for n = 1..10000 computed as part of the research on 4-dimensional point groups.