Extending Steinitz’s Theorem to Upward Star-Shaped Polyhedra and Spherical Polyhedra

2011/09/20 by Seok-Hee Hong, Hiroshi Nagamochi · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Advanced Materials and Mechanics #Algorithm #Characterization (materials science) #Combinatorics #Computational Geometry and Mesh Generation #Convex optimization #Convex polytope #Convex set #Dual polyhedron #Geometry #Graph #Integer points in convex polyhedra #Linear programming #Mathematical analysis #Mathematics #Physics #Planar graph #Polyhedron #Regular polygon #Star (game theory) #Vertex (graph theory)

paper · doi:10.1007/s00453-011-9570-x

published in Algorithmica 61(4), 1022-1076 (Springer Science and Business Media LLC)

openalex publication_date 2011/09/20 · crossref created 2011/09/20 · crossref issued 2011/09/21 · crossref published 2011/09/21 · crossref published-online 2011/09/21 · crossref published-print 2011/12/01 · crossref deposited 2023/06/09 · crossref indexed 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Citations

• XLV. On reciprocal figures and diagrams of forces
• Abstract Regular Polytopes
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• Drawing stressed planar graphs in three dimensions
• Lectures on Polytopes Updated Seventh Printing of the First Edition
• On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs
• Graphs of polyhedra; polyhedra as graphs
• Puzzles and polytope isomorphisms
• Dividing a Graph into Triconnected Components
• Convex Representations of Graphs
• On-line maintenance of triconnected components with SPQR-trees
• On-Line Planarity Testing
• A polynomial time circle packing algorithm
• A simple way to tell a simple polytope from its graph
• How to Draw a Graph
• On the delta‐wye reduction for planar graphs
• Reconstructing a Simple Polytope from its Graph
• How to cage an egg

Cited by

• Steinitz's theorem [wikipedia]