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287:. . . the small cubicuboctahedron can be interpreted as a coloring of the regular (not just uniform) tiling of the genus 3 surface by 20 equilateral triangles, meeting at 24 vertices, each with degree 7. This regular tiling is significant as it is a tiling of the Klein quartic, the genus 3 surface . . .
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As the Euler characteristic suggests, the small cubicuboctahedron is a toroidal polyhedron of genus 3 (topologically it is a surface of genus 3), and thus can be interpreted as a (polyhedral) immersion of a genus 3 polyhedral surface. Stated alternatively, it corresponds to a uniform tiling of this
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an immersion, polyhedral or otherwise, of a surface. For, at each of its 24 vertices, the picture locally is that of a cone on a figure-8 (just as the cross-cap has one of these), and even one of these means the polyhedron is not immersed in 3=space. The underlying polyhedron
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But there is no such tiling of the surface of genus 3. (For, the number of vertices would have to be 3*20 / 7, which is not only unequal to 24, but it is not even an integer.)
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correspond to a uniform tiling of the surface of genus 3. But the second sentence's claim that it is the first sentence "Stated alternatively", is also incorrect.
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This is *not* a polyhedrally "immersed" surface -- nor can that be "Stated alternatively" to say it is a uniform tiling (although it is)
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Knowledge. If you would like to participate, please visit the project page, where you can join
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TBH I never really liked
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I understand what is intended, but that's the extended Schläfli symbol for the
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