A Polyhedron Full of Surprises

2012/11/29 by Hans L. Fetter · 1 citation
Computer Science · Mathematics · Engineering · #Computational Geometry and Mesh Generation #Advanced Combinatorial Mathematics #graph theory and CDMA systems #Polyhedron #Mathematics #Vertex (graph theory) #Regular polygon #Combinatorics #Convex polytope #Tangent #Enhanced Data Rates for GSM Evolution #Realization (probability) #Geometry #Convex set #Computer science #Convex optimization #Artificial intelligence

paper · doi:10.4169/math.mag.85.5.334

openalex publication_date 2012/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06

Abstract

SummaryThe problem of geometric realization for convex polyhedra, which satisfy certain desirable properties, has received quite a bit of attention lately. Interest, mainly, has been on polyhedral representations where either all of the vertex coordinates are small integers, or all of the edge lengths are integers, or all of the edges are tangent to a sphere. In general, it is not easy to construct a convex polyhedron satisfying any of those criteria. We introduce a remarkable polyhedron that satisfies all of them.

Citations

• Dual Models
• Graphs of polyhedra; polyhedra as graphs
• T. P. Kirkman, Mathematician

Cited by

• Midsphere [wikipedia]

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