An enduring error

DOI10.4171/EM/120zbMath1176.52002OpenAlexW1969412460WikidataQ55877844 ScholiaQ55877844MaRDI QIDQ835322

Branko Grünbaum

Publication date: 28 August 2009

Published in: Elemente der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/em/120

zbMATH Keywords

uniform polyhedronArchimedean solidsemiregular polyhedronMiller's solidpseudorhombicuboctahedron

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Polyhedra and polytopes; regular figures, division of spaces (51M20) Symmetry properties of polytopes (52B15)

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Optimal finite homogeneous sphere approximation ⋮ Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles ⋮ Quasi-vertex-transitive maps on the plane ⋮ The Bilinski dodecahedron and assorted parallelohedra, zonohedra, monohedra, isozonohedra, and otherhedra ⋮ Platonic stars ⋮ Semi-regular tilings of the hyperbolic plane ⋮ Platonic solids, Archimedean solids and semi-equivelar maps on the sphere ⋮ Representing the sporadic Archimedean polyhedra as abstract polytopes

Uses Software

• Mathematica
• Kaleido

Cites Work

• On the Archimedean or semiregular polyhedra
• Isogonal prismatoids
• Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler
• Characterizing the vertex neighbourhoods of semi-regular polyhedra
• The complete set of uniform polyhedra
• An enumeration of simplicial 4-polytopes with 8 vertices
• Uniform polyhedra
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