The number of convex tilings of the sphere by triangles, squares, or hexagons

DOI10.2140/gt.2018.22.2839zbMath1393.52012arXiv1702.02614OpenAlexW2783425288WikidataQ129710803 ScholiaQ129710803MaRDI QIDQ1637314

Peter Smillie, Philip Engel

Publication date: 8 June 2018

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02614

zbMATH Keywords

polyhedraspheremodular formtriangulationstilingnonnegative curvatureshapes of polyhedraThurston

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (5)

Acute Geodesic Triangulations of Manifolds ⋮ Volume forms on moduli spaces of \(d\)-differentials ⋮ Intersection theory and volumes of moduli spaces of flat metrics on the sphere ⋮ On the growth rate of the number of fullerenes ⋮ Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares

Cites Work

• The complex Lorentzian Leech lattice and the bimonster
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• The Leech lattice and complex hyperbolic reflections
• New complex- and quaternion-hyperbolic reflection groups
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Generalized Picard lattices arising from half-integral conditions
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• Indefinite quadratische Formen und Funktionentheorie. II
• A Census of Planar Triangulations
• Convex Polyhedra

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