# Template:632 symmetry table

In geometry, the [6,3], (*632) symmetry group is bounded by mirrors meeting with angles of 30, 60, and 90 degrees. There are a number of small index subgroups constructed by mirror removal and alternation. h[6,3] = [1^{+},6,3] creates [3^{[3]}], (*333) symmetry, shown as red mirror lines. Removing mirrors at the order-3 point creates [6,3^{+}], 3*3 symmetry, index 2. Removing all mirrors creates [6,3]^{+} (632) subgroup, index 2. The communtator subgroup is [1^{+},6,3^{+}], (333) symmetry, index 4. An index 6 subgroup constructed as [6,3*], also becomes (*333), shown in blue mirror lines, and which has its own (333) rotational symmetry, index 12.