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Do the lazy caterer's sequence (cutting a 2-cube into pieces) and cake numbers (cutting a 3-cube into pieces) extend naturally to higher dimensions? In general, is the "hypercake sequence" in n dimensions given by ?
And since these sequences are for hypercubes only, what happens for other polytopes? You can topologically transform any convex polytope into any other, and so they should have the same sequences, but what about toroidal polytopes and other non- simply connected polytopes? Double sharp ( talk) 09:24, 12 August 2012 (UTC)
In polychora, the vertex figure is a polyhedron. The faces of these polyhedra are polygons, which are themselves vertex figures of the polyhedra that are the cells of the polychoron. Does the vertex figure contain the information necessary to write the " edge configuration" (analogous to the vertex configuration for polyhedra) of polyhedra surrounding an edge of the polychoron? And does this hold further for all n-polytopes? Double sharp ( talk) 10:42, 12 August 2012 (UTC)
Mathematics desk | ||
---|---|---|
< August 11 | << Jul | August | Sep >> | August 13 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Do the lazy caterer's sequence (cutting a 2-cube into pieces) and cake numbers (cutting a 3-cube into pieces) extend naturally to higher dimensions? In general, is the "hypercake sequence" in n dimensions given by ?
And since these sequences are for hypercubes only, what happens for other polytopes? You can topologically transform any convex polytope into any other, and so they should have the same sequences, but what about toroidal polytopes and other non- simply connected polytopes? Double sharp ( talk) 09:24, 12 August 2012 (UTC)
In polychora, the vertex figure is a polyhedron. The faces of these polyhedra are polygons, which are themselves vertex figures of the polyhedra that are the cells of the polychoron. Does the vertex figure contain the information necessary to write the " edge configuration" (analogous to the vertex configuration for polyhedra) of polyhedra surrounding an edge of the polychoron? And does this hold further for all n-polytopes? Double sharp ( talk) 10:42, 12 August 2012 (UTC)