Mathematics Research Projects

Project 13: Drawing Graphs

It is possible to represent a convex 3-dimensional polytope by a graph in the plane. Such graphs can be plane graphs (i.e. have crossings only at vertices) or show crossings. It may be desirable for a drawing to have crossings if by doing so it displays some aspect of the original polytope, for example, more of its symmetries.


1. Examine the relation between the isometries of 3-dimensional polytopes and the symmetries that are displayed by different graphs that might be used to represent them, with or without crossings, in the plane. As specific examples one might consider drawings of the tetrahedron, cube, and octahedron in the the plane.

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Joseph Malkevitch
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451-0001
(Comments and results related to the project above are welcome.)

Some of this work was prepared with partial support from the National Science Foundation (Grant Number: DUE 9555401) to the Long Island Consortium for Interconnected Learning (administered by SUNY at Stony Brook, Alan Tucker, Project Director).