Rational-angle a^4b pentagonal sphere tilings are exactly three families: a 12-tile tetrahedral subdivision, a 4m-tile symmetric family with flips, and a 20-tile non-symmetric case.
Moduli Spaces of Pentagonal Subdivision Tilings
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abstract
Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two dimensional moduli. We describe the moduli in detail.
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Tilings of the sphere by congruent pentagons V: Edge combination $a^{4}b$ with rational angles
Rational-angle a^4b pentagonal sphere tilings are exactly three families: a 12-tile tetrahedral subdivision, a 4m-tile symmetric family with flips, and a 20-tile non-symmetric case.