Melzak's Conjecture seeks the polyhedron with minimal perimeter for a given volume. In studying this problem, the first approach may be to compare different polyhedra with a unit volume. However, the wide array of volume formulas for polyhedra make a unit volume computationally cumbersome. Instead, a more efficient approach is to consider the ratio of edge length to volume. In this manner, one may assign the edge length or volume to conveniently fit the situation. This paper summarizes previous work on the problem and presents some experimental observations from recent research. Much work is presented on ideas centered around prisms and their properties, and ideas for future consideration are explained, offering contributions to the ongoing study of Melzak's Conjecture.
Debra Mimbs, Associate Professor of Mathematics, Lee University
Burk, Kaitlyn; Carty, Adam; and Wheeler, Austin
"A Study of the Shortest Perimeter Polyhedron,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18
, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss2/3