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).