Pictures below are from the workshop held at the ICME-13. All these figures have the Euler characteristic of a torus, i.e. V-E+F=0.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhD4MuMINePqE33C5t0f5ry8mTMaDPZQbQ1z8ZO0gmTpyAb7SF8ubtcmW21YtrtZLig78To6FtBMX2Cjfn3sMIuPR7L5MXGoJ5kwUcR2K5sw8t2dvi41lSkIiqtAHQr2n1mPGd1sR496eG/s640/13838025_10154213980468280_716421611_o.jpg)
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Torus inspired by triangulation found by Sarah-Marie Belcastro
This torus has 42 faces (12 pentagons, 24 hexagons and 6 octagons), 126 edges, and 84 vertices, which gives you Euler characteristic V-E+F=0.
Here are some more simple toroids with hexagons, octagons, decagons, and squares: ![]() ![]() ![]() ![]()
Can you make others? Send us and will be published here!
Some references:
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