K3 period data is a quadruple $(\Lambda,(\cdot,\cdot),H^{2,0},{\cal K})$ consisting of a free abelian group $\Lambda$, a symmetric pairing $(\cdot,\cdot):\Lambda\times\Lambda\to{{\bf Z}}$, a $1$-dimensional complex vector subspace $H^{2,0}\subset\Lambda\otimes{{\bf C}}$ and a set ${\cal K}\subset\Lambda\otimes{{\bf R}}$ satisfying the following conditions:

1. 1.

   $rk\,\Lambda=22$;

2. 2.

   $(\Lambda,(\cdot,\cdot))$ is isomorphic to $\Lambda_{K3}$;

3. 3.

   for any $v\in H^{2,0}\setminus\{0\}$ one has $(v,v)=0$ and $(v,\overline{v})>0$;

4. 4.

   the set ${\cal K}$ is a connected component of $C\setminus\cup_{v\in\Lambda,(v,v)=-2,(v,H^{2,0})=0}H_{v}\,$, where $C=\{w\in\Lambda\otimes{{\bf R}}|(w,H^{2,0})=0,(w,w)>0\}$ and $H_{v}$ is the hyperplane orthogonal to $v$.