Document Type
Article
Publication Date
8-30-2024
First Advisor
Joshua Holden
Abstract
The SOMA Cube is a puzzle toy in which seven irregularly shaped blocks must be fit together to build a cube. There are 240 distinct solutions to the SOMA Cube. One rainy afternoon, Conway and Guy created a graph of all the solutions by manually building each solution. They called their graph the SOMAP. We studied how the geometric structure of the SOMA Cube pieces informs the graph theoretic properties of the SOMAP, such as subgraphs that can or cannot appear and vertex centrality. We have also used permutation group theory to decipher notation used by Knuth in previous work on the SOMAP.
Recommended Citation
Asbury, Kyle and Glancy, Ben, "Graph and Group Theoretic Properties of the SOMA Cube and SOMAP" (2024). Mathematical Sciences Technical Reports (MSTR). 185.
https://scholar.rose-hulman.edu/math_mstr/185