Mathematics Research Projects

Project 17: Nets and Truncation

A net of a polytope P is a planar pattern of polygons N that can be folded by identifying edges of the boundary of N into polytope P.


1. Suppose that a complete set of nets is available for some polytope P. Suppose vertex v of the polytope P is truncated so that the resulting polytope P' has as regular a polygon as possible resulting from the truncation at v. Is there any relation between the nets of P' and the nets of P?

Test case: Find all the nets of a square pyramid. Find all the nets which arise when the 4-valent vertex of the pyramid is truncated to give a square.

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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).