Solutions to the 4-color problem on sphere triangulations with degree sequence 6,6,6,6,6,6,4,4,4,4,4,4 are sorted into types parametrized by lattice points in 4D polyhedral cones, with an integral quadratic form counting triangles and related to Thurston's flat cone moduli space.
This is the same factor that comes up for Q
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not complete: collisions between vertices take place a finite distance from a nonsingular point. The metric completion is a complex hyperbolic cone-manifold. In some interesting special cases, the metric completion is an orbifold. The concrete description of these spaces of shapes gives information about the combinatorial classification of triangulations of the sphere with no more than 6 triangles at a vertex.
fields
math.MG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Baez outlines Thurston's results constructing triangulations of the sphere via Eisenstein integers and shows the moduli space of associated flat metrics is open and dense in an orbifold defined by a quadratic form on C^10.
citing papers explorer
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The Four Color Theorem meets Shapes of Polyhedra
Solutions to the 4-color problem on sphere triangulations with degree sequence 6,6,6,6,6,6,4,4,4,4,4,4 are sorted into types parametrized by lattice points in 4D polyhedral cones, with an integral quadratic form counting triangles and related to Thurston's flat cone moduli space.
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Triangulations of the Sphere
Baez outlines Thurston's results constructing triangulations of the sphere via Eisenstein integers and shows the moduli space of associated flat metrics is open and dense in an orbifold defined by a quadratic form on C^10.