The Roundest Polyhedra with Symmetry Constraints
AbstractAmongst the convex polyhedra with n faces circumscribed about the unit sphere, which has the minimum surface area? This is the isoperimetric problem in discrete geometry which is addressed in this study. The solution of this problem represents the closest approximation of the sphere, i.e., the roundest polyhedra. A new numerical optimization method developed previously by the authors has been applied to optimize polyhedra to best approximate a sphere if tetrahedral, octahedral, or icosahedral symmetry constraints are applied. In addition to evidence provided for various cases of face numbers, potentially optimal polyhedra are also shown for n up to 132. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Lengyel, A.; Gáspár, Z.; Tarnai, T. The Roundest Polyhedra with Symmetry Constraints. Symmetry 2017, 9, 41.
Lengyel A, Gáspár Z, Tarnai T. The Roundest Polyhedra with Symmetry Constraints. Symmetry. 2017; 9(3):41.Chicago/Turabian Style
Lengyel, András; Gáspár, Zsolt; Tarnai, Tibor. 2017. "The Roundest Polyhedra with Symmetry Constraints." Symmetry 9, no. 3: 41.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.