User talk:Parcly Taxel

Welcome to Wikimedia Commons, Parcly Taxel!

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-- Wikimedia Commons Welcome (talk) 10:25, 4 October 2014 (UTC)

9-coloured triple torus

Update

Hi Parcly Taxel,

Thanks for uploading the SVG files. I highly admire your ability to find the colourings. Hope you don't mind my redrawing File:9_mutually_adjacent_regions_on_triple_torus_2.svg to make the regions 120° apart at the holes, avoid the pseudoquadripoints, and more clearly distinguish the regions for colour-blind people.

Cheers, cmɢʟee ⋅τaʟκ 13:15, 11 October 2024 (UTC)

I don't mind your redrawing; I included the pseudoquadripoints to stay true to the primal graph formulation and because (for the second K₉ map) they preserve a reflection symmetry of the uncoloured regions.

Primal

Dual

I have uploaded K₁₂ embedded vertex-transitively (chiral tetrahedral symmetry) into the genus 6 orientable surface. Euler's formula shows that in this case every face must be a triangle, with no pseudoquadripoints in the dual map. Parcly Taxel 01:12, 13 October 2024 (UTC)

Thanks, Taxel. I totally understand that these points look tidier, though am concerned that they might confuse someone less familiar with the topic who might assume regions diagonally across are considered adjacent.

Great of you to upload these maps. I don't understand your statement that every face must be a triangle as quite a few of them in the thumbnail don't appear so.

Cheers, cmɢʟee ⋅τaʟκ 08:45, 13 October 2024 (UTC)

Topologically they are triangles – they are bounded by three edges and three vertices. Geometrically, of course they aren't. Parcly Taxel 10:34, 13 October 2024 (UTC)

Got it. Thanks for explaining, cmɢʟee ⋅τaʟκ 19:35, 13 October 2024 (UTC)