### 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.

**Problem**

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

email: malkevitch@york.cuny.edu

(Comments and results related to the project above are welcome.)

**Acknowledgements**

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).