Established in 2008, the SOAR Program is an opportunity for students in the Department of Mathematics at Grove City College to participate in a short-term, focused research project. For four weeks each summer the College invites three math students to work on a research project. The SOAR Program is generously funded by Grove City College's Swezey Fund for Scientific Research and Instrumentation. The Department of Mathematics continues the SOAR Program based upon adequate levels of support.
Over the last six years, the SOAR Program has been investigating polytope numbers which are number sequences created from the geometry of polytopes.
Building on the work of H.K. Kim of Pohang University in Korea, student researchers in the SOAR Program have found various formulae for polytope number sequences. Work has included investigating polytope number sequences for polytopes created by various operations such as rectification (cutting off each vertex to the middle of the adjacent edges), r-rectification (cutting off each vertex to the middles of each adjacent r-facet), as well as expansion (replacing each edge by a square face and adding other edges and vertices are necessary). In many cases, our students were able to write these polytope number sequences as linear combinations of simplex number sequences, and to generalize the work of polytope number sequences to non-spherical polytopes in both dimensions 3 and 4. During the summer of 2013, the SOAR Program developed a method to step up to compute polytope number sequences in order to extend work beyond where H.K. Kim’s process could be initially applied. The SOAR Program continues in its efforts to modify the stepping up process to work in more situations.
Our students have participated in REU programs across the country including: