Dissertations, Theses, and Capstone Projects
Date of Degree
10-2014
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Joseph Malkevitch
Subject Categories
Mathematics
Keywords
Eberhard, Polyiamond, triangle
Abstract
Polyiamonds are plane geometric figures constructed by pasting together equilateral triangles edge-to-edge. It is shown that a diophantine equation involving vertices of degrees 2, 3, 5 and 6 holds for all polyiamonds; then an Eberhard-type theorem is proved, showing that any four-tuple of non-negative integers that satisfies the diophantine equation can be realized geometrically by a polyiamond. Further combinatorial and graph-theoretic aspects of polyiamonds are discussed, including a characterization of those polyiamonds that are three-connected and so three-polytopal, a result on Hamiltonicity, and constructions that use minimal numbers of triangles in realizing four-vectors.
Recommended Citation
Larson, Christopher, "Combinatorial Properties of Polyiamonds" (2014). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/441