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This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Peter Saveliev

More: This symmetry is supposed to be an involution of the $3$-space; therefore its diagonalized matrix has only $\pm 1$ on the diagonal. With an even number of $-1$s you have two right (or two left) hands. With an odd number of $-1$s you have a right and a left hands. However, a single $-1$ gives us a mirror symmetry: pen draws pen. We are left with a single option: three $-1$s, i.e., the central symmetry.