Template:632 symmetry table

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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.

Wallpaper subgroup relationships[edit]

References[edit]

  1. ^ Coxeter, (1980), The 17 plane groups, Table 4
  • Coxeter, H. S. M. & Moser, W. O. J. (1980). Generators and Relations for Discrete Groups. New York: Springer-Verlag. ISBN 0-387-09212-9.