Let L_{2 }be an orthogonal lattice in a plane q and F a figure in q. We define that F has the l.p.c.p.(lattice point covering property) if for every position of F in the plane, the figure F includes at least one lattice point.

It is very simple to see that the circle c_{0} of diameter 2R=2^{1/2} has the l.p.c.p. So every figure including c_{0} has the l.p.c.p. For example the equilateral triangle including c_{0} has side equal to 2.449 and obviously has the l.p.c.p. Nevertheless we can prove that an equilateral triangle with side 2.154 has l.p.c.p. That is, the problem is to find the minimum conditions between the elements of the figure F, so that the figure F to be able for the l.p.c.p.

Another example for L_{3}. A cube of side 3^{1/2} has obviously the l.p.c.p. because includes a sphere of diameter 3^{1/2}. But it has been proved by M. Henk that a cube of side 2^{1/2} has the l.p.c.p. Remains open the problem for n-cube. M. Henk and the author solved the problem for the ellipsoid in L_{n} and here is the solution for l.p.c.p. of the ellipse in the plane.