In finite geometry, the Fano plane is the finite projective plane with the smallest possible number of points and lines: 7 each.
Why its automorphism group is $PSL(2,\mathbb{F}_7)$?
For the platonic solids, their automorphism group (orientation preserving) are $A_4, S_4$, and $A_5$. For the Fano plane, can we consider automorphisms which preserve orientation? (i.e. is the group $PSL(2,\mathbb{F}_7)$ orientation preserving?)