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Tuesday, March 5, 2019

The Eightfold Cube and PSL(2,7)

Filed under: General,Geometry — Tags: , — m759 @ 10:45 PM

For PSL(2,7), this is ((49-1)(49-7))/((7-1)(2))=168.

The group GL(3,2), also of order 168, acts naturally
on the set of seven cube-slicings below —

Another way to picture the seven natural slicings —

Application of the above images to picturing the
isomorphism of PSL(2,7) with GL(3,2) —

Why PSL(2,7) is isomorphic to GL(3.2)

For a more detailed proof, see . . .

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