Polytopes are the generalizations of polygons and polyhedra. In this project, we model polytopes as graphs, with each edge being an identical resistor, and calculate the equivalent resistance between two arbitrary nodes. We explore four methods to solve for equivalent resistances, based on the work of Kirchhoff, van Steenwijk, Lovász, and Nahin. We present results for the Platonic solids, selected Archimedean solids, and all but one of the regular convex four-dimensional polytopes. The project then concludes with an overview of opportunities for future research, including extending these strategies to the Catalan solids.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Stern, Kevin E.

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-050521-144424
• 22281

Keyword

• resistor network
• polytope
• random walk
• equivalent resistance

Award

• Provost's MQP Award

Advisor

• Servatius, Brigitte
• Aravind, Padmanabhan K.

Year

• 2021

Date created

• 2021-05-05

Resource type

• Major Qualifying Project

Major

• Physics

Rights statement

• In Copyright

License

• All rights reserved

Last modified

• 2023-01-19