
We develop the theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those related to pentagonal or double pentagonal subdivisions.
FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05B45
FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05B45
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