https://conwaylife.com/w/index.php?title=Symmetry&oldid=70858
15 total symmetries, not counting D8_2 which i feel is not a symmetry, and also not counting C1 (no symmetry).
symmetry matters when searching among initial states in Conway's Game of Life because symmetry is never lost.
enumerate symmetries for other tessellations and honeycombs.
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