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
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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.
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