Symmetry

One class per symmetry group, labeled by Conway orbifold symbol (digits descending: 532 and *532 for the chiral and full icosahedral groups), computed from the combinatorial automorphisms, which act as isometries by uniqueness of the realization. Up to 8 exemplars per class, smallest first.

*532 — order 120, with reflections — 8 built nets

532 — order 60, chiral — 4 built nets

*432 — order 48, with reflections — 8 built nets

432 — order 24, chiral — 4 built nets

*332 — order 24, with reflections — 26 built nets

*622 — order 24, with reflections — 13 built nets

2*6 — order 24, with reflections — 3 built nets

*522 — order 20, with reflections — 13 built nets

2*5 — order 20, with reflections — 2 built nets

*422 — order 16, with reflections — 1 built nets

2*4 — order 16, with reflections — 2 built nets

332 — order 12, chiral — 19 built nets

622 — order 12, chiral — 4 built nets

*322 — order 12, with reflections — 31 built nets

2*3 — order 12, with reflections — 7 built nets

522 — order 10, chiral — 5 built nets

*222 — order 8, with reflections — 35 built nets

2*2 — order 8, with reflections — 22 built nets

322 — order 6, chiral — 8 built nets

*33 — order 6, with reflections — 28 built nets

222 — order 4, chiral — 22 built nets

*22 — order 4, with reflections — 112 built nets

2* — order 4, with reflections — 10 built nets

2x — order 4, with reflections — 1 built nets

33 — order 3, chiral — 4 built nets

22 — order 2, chiral — 229 built nets

* — order 2, with reflections — 208 built nets

x — order 2, with reflections — 2 built nets

1 — order 1, chiral — 1395 built nets