If you cut out this star, you can fold it into a polyhedron where all 11 of its tips meet at one point. This polyhedron will be tiled by the small gray equilateral triangles, though some may get bent. There will be 12 points where five such triangles meet: the 11 indentations in the star, and the point where all its tips meet. There are also points where six triangles meet. This may seem like a curiosity, but Bill Thurston discovered some profound facts about stars of this sort.
John Baez (Tue,) studied this question.