### Mathematics Research Projects

## Project 21: Polyhedra Folded
from Isosceles Right Triangles

**Problem**:

1. What convex 3-polytopes can be created which have as their
faces congruent isosceles right triangles?

2. What convex 3-polytopes can be created which have as their
faces the union of congruent isosceles right triangles? (Example:
A cube.)

3. What convex 3-polytopes can be created which have as their
faces congruent right triangles?

4. What convex 3-polytopes can be created which have as their
faces the union of congruent right triangles?

5. What convex 3-polytopes can be created which have as their
faces the union of right triangles?

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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).