A combinatorial theorem for a symmetric triangulation of the sphere \(S^2\). (English) Zbl 1003.05033

Summary: We prove a combinatorial lemma from which it follows that the set \(g^{-1}(0)\) of zeros of a continuous and odd function \(g: S^2\to R\), \(g(-x)= -g(x)\), from the 2-dimensional sphere \(S^2\) contains a symmetric component.


05B45 Combinatorial aspects of tessellation and tiling problems
52B70 Polyhedral manifolds
57Q15 Triangulating manifolds
Full Text: EuDML