Non-existence of polyhedral immersions of triangulated surfaces in \(\mathbb R^3\) (Q2400116)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-existence of polyhedral immersions of triangulated surfaces in \(\mathbb R^3\) |
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Non-existence of polyhedral immersions of triangulated surfaces in \(\mathbb R^3\) (English)
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28 August 2017
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The author constructs two vertex-minimal 9-vertex triangulations of the non-orientable surface of genus 5 and shows that neither of them is polyhedrally immersible in \(\mathbb R^3\). These two neighborly triangulations are both of Schläfli type \(\{3, 8\}\), with automorphism groups \(\mathbb Z_6\) and \(S_3\times \mathbb Z_3\), respectively.
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non-orientable surface
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triangulation
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geometric realization
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polyhedral immersion
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self-intersection
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obstruction
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neighborly
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Heawood bound
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threefold geometric symmetry
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