Icosahedra constructed from congruent triangles

Published

Journal Article

It is possible to construct a figure in three dimensions which is combinatorially equivalent to a regular icosahedron, and whose faces are all congruent but not equilateral. Such icosamonohedra can be convex or nonconvex, and can be deformed continuously. A scalene triangle can construct precisely zero, one, or two convex icosamonohedra, and each occurs. Demonstrated here are two explicit convex examples, the first of which is the unique such object constructed from scalene right triangles, proving a conjecture of Banchoff and Strauss.

Full Text

Duke Authors

Cited Authors

  • Miller, EN

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 24 / 2-3

Start / End Page

  • 437 - 451

International Standard Serial Number (ISSN)

  • 0179-5376

Digital Object Identifier (DOI)

  • 10.1007/s004540010047

Citation Source

  • Scopus