Symmetry Td (tetrahedral)

OrderCount
32
42
52
61

Symmetry Oh (octahedral)

OrderCount
37
49
526
643
780
872
947

Symmetry Ih (icosahedral)

OrderCount
311
442
5285
61579
79354
845471
9200324
10622944(?)
11?
12?
13?
14?
15?