Spherical Tiling by 12 Congruent Pentagons

Details Spherical Tiling by 12 Congruent Pentagons Spherical Tiling by 12 Congruent Pentagons

2010-09-13

arxiv.org/abs/1009.2361v2

Mathematics

Combinatorics

56 pages, 45 figures, spherical geometry

Scientific paper

The edge-to-edge tiling of the 2-dimensional sphere by congruent pentagons must contain at least 12 tiles. We give almost complete classification of the minimal tiling by 12 congruent pentagons, with the only unsolved problem being some very specific spherical geometrical problem. This is done by first separately classifying the combinatorial, edge length, and angle aspects of the tiling, and then combining the respective classifications together.

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