Computing Maximal Copies of Polyhedra Contained in a Polyhedron

DOI10.1080/10586458.2014.956374zbMath1315.51017arXiv1407.0683OpenAlexW3098361044MaRDI QIDQ5246363

Moritz Firsching

Publication date: 21 April 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0683

zbMATH Keywords

polytopesnonlinear optimizationcopies of polyhedra

Mathematics Subject Classification ID

Nonlinear programming (90C30) Polyhedra and polytopes; regular figures, division of spaces (51M20) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

Realizability and inscribability for simplicial polytopes via nonlinear optimization ⋮ On the circuit diameter conjecture ⋮ Small covers and quasitoric manifolds over neighborly polytopes

Uses Software

• PARI/GP
• SageMath
• SCIP
• SciPy

Cites Work

• Unnamed Item
• On a problem of Croft on optimally nested regular polygons
• SCIP: solving constraint integer programs
• Large regular simplices contained in a hypercube
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• Unsolved problems in geometry
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• Largest placement of one convex polygon inside another
• Largest \(j\)-simplices in \(d\)-cubes: Some relatives of the Hadamard maximum determinant problem
• On Maximal Regular Polyhedra Inscribed in a Regular Polyhedron
• Constraint Integer Programming: A New Approach to Integrate CP and MIP