Visualizing Convex Regular-Faced Polyhedra through 3D Printing

Authors

Presenter(s)

Elizabeth Paci

Comments

Presentation: 9:00-10:15 a.m., Kennedy Union Ballroom

Files

Description

Hilbert’s third problem asks whether two polyhedra of equal volume are scissors-congruent. In other words, is it possible to slice one of the polyhedra into a finite number of polyhedra and then rearrange them to form the other polyhedron. Dehn showed that this is not the case by creating a polyhedra invariant now named in his honor: the Dehn invariant. One may show that two polyhedra are scissors-congruent if and only if they have the same volume and Dehn invariant. A related topic concerns whether it’s possible to slice a convex regular-faced polyhedra into a finite number of solids which are themselves convex regular-faced polyhedra. Examples of regular-faced polyhedra include the Platonic, Archimedean, and Johnson solids. We will discuss how these and related ideas—including the nomenclature of polyhedra—can be visualized using 3d printing techniques.

Publication Date

4-19-2023

Project Designation

Capstone Project

Primary Advisor

George Todd

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium, College of Arts and Sciences

Institutional Learning Goals

Scholarship

Recommended Citation

"Visualizing Convex Regular-Faced Polyhedra through 3D Printing" (2023). Stander Symposium Projects. 3201.
https://ecommons.udayton.edu/stander_posters/3201