Polyhedral realization in \(R^ 3\) of triangulations of the torus and 2- manifolds in cyclic 4-polytopes

DOI10.1016/0012-365X(71)90011-2zbMath0235.57001MaRDI QIDQ2551991

Amos Altshuler

Publication date: 1971

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

Mathematics Subject Classification ID

Embeddings and immersions in topological manifolds (57N35) Triangulating manifolds (57Q15)

Related Items

Enumeration of platonic maps on the torus ⋮ Spatial polyhedra without diagonals ⋮ Permuted difference cycles and triangulated sphere bundles ⋮ Equivelar polyhedral manifolds in \(E^ 3\). ⋮ On valences of polyhedra ⋮ Neighborly maps with few vertices ⋮ A non‐Schlegelian polyhedral map on the torus ⋮ Combinatorial 3-manifolds with transitive cyclic symmetry ⋮ Partitioning the triangles of the cross polytope into surfaces ⋮ Bänder und Möbiusbänder in konvexen Polytopen ⋮ Flache Einbettungen geschlossener Mannigfaltigkeiten der Kodimension 1 in Randkomplexe konvexer Polytope ⋮ Polyedrische 2-Mannigfaltigkeiten mit wenigen nichtkonvexen Ecken ⋮ Geometric coloring theory ⋮ Hamilton-Flächen auf Prismen ⋮ Hamiltonian circuits in some maps on the torus ⋮ Construction and enumeration of regular maps on the torus ⋮ Nonconvex vertices of polyhedral 2-manifolds ⋮ Degree-regular triangulations of torus and Klein bottle ⋮ Higherdimensional analogues of Császár's torus ⋮ Neighborly combinatorial 3-manifolds with dihedral automorphism group ⋮ The number of simplicial neighbourly d ‐polytopes with d +3 vertices ⋮ On weakly neighborly polyhedral maps of arbitrary genus

Cites Work

• Preassigning the shape of a face
• Manifolds in stacked 4-polytopes
• Hamiltonian circuits in some maps on the torus
• SOLUTION OF THE HEAWOOD MAP-COLORING PROBLEM
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