50 vertices arranged in D6 symmetry is interesting in that it forms two different but close in length triangle strips -- one following the longitudes and the other the latitudes.

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And 22 vertices can also arrange with 2-fold cylindrical symmetry that runs all the pentagons together into one long strip. It produces one long triangle strip and three short ones.

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22 vertices can also arrange with 2-fold dihedral symmetry with two strips of six pentagons each separated by a single loop of 10 hexagons. The triangulation has two long triangle strips and two short ones.

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40 vertices in tetrahedral symmetry gives a mix of the two with 4 strips that wrap twice and three that only wrap once.

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22 vertices can also have tetrahedral symmetry, but now only have four strips that each wrap the sphere twice.

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16 vertices gives a triangulation with tetrahedral symmetry. It has 7 triangle strips.

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In contrast, the 12-vertex icosahedron has 6 triangle strips.

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