11. In chemical laboratories, floors are covered with tiles made of acid-resistant ceramic, which have the shape of regular polygons. Which polygons can fill the floor plane without gaps
11. The internal angle of a regular polygon is equal to $\frac{2 d(n-2)}{n}, n$-the number of sides. Let $x$ polygons meet at one vertex, then $\frac{2 d(n-2)}{n} x=4 d$, from which $x=\frac{2 n}{n-2}=2+\frac{4}{n-2}$. This number must be an integer, i.e., $\frac{4}{n-2}$ must be an integer.

A polygon can have no fewer than three sides, so $n>2$. But $n-2 \leqslant 4$, i.e., $n \leqslant 6$. The number 5 does not work, as in this case the expression $\frac{4}{n-2}$ would be a fraction. Thus, $n_{1}=3 ; n_{2}=4 ; n_{3}=6$, i.e., the plane can be filled without gaps by regular triangles, squares, and regular hexagons.