Corollary

*Let $H$ and $H'$ be two distinct, parallel, non-isotropic hyperplanes. If $K$ is of characteristic zero (resp. $p > 0$, with $p \neq 2$), the group of displacements of $E$ generated by $s_H$ and $s_{H'}$ is an infinite dihedral group (resp. a dihedral group of order $2p$).

Indeed, by Prop. 2 of Chap. IV, § 1, no. 2, it suffices to show that $s_{H'} s_H$ is of infinite order (resp. order $2p$), which is clear.