Icosahedra constructed from congruent triangles
Publication
, Journal Article
Miller, EN
Published in: Discrete and Computational Geometry
January 1, 2000
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.
Duke Scholars
Published In
Discrete and Computational Geometry
DOI
ISSN
0179-5376
Publication Date
January 1, 2000
Volume
24
Issue
2-3
Start / End Page
437 / 451
Related Subject Headings
- Computation Theory & Mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Miller, E. N. (2000). Icosahedra constructed from congruent triangles. Discrete and Computational Geometry, 24(2–3), 437–451. https://doi.org/10.1007/s004540010047
Miller, E. N. “Icosahedra constructed from congruent triangles.” Discrete and Computational Geometry 24, no. 2–3 (January 1, 2000): 437–51. https://doi.org/10.1007/s004540010047.
Miller EN. Icosahedra constructed from congruent triangles. Discrete and Computational Geometry. 2000 Jan 1;24(2–3):437–51.
Miller, E. N. “Icosahedra constructed from congruent triangles.” Discrete and Computational Geometry, vol. 24, no. 2–3, Jan. 2000, pp. 437–51. Scopus, doi:10.1007/s004540010047.
Miller EN. Icosahedra constructed from congruent triangles. Discrete and Computational Geometry. 2000 Jan 1;24(2–3):437–451.
Published In
Discrete and Computational Geometry
DOI
ISSN
0179-5376
Publication Date
January 1, 2000
Volume
24
Issue
2-3
Start / End Page
437 / 451
Related Subject Headings
- Computation Theory & Mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics