Unions of regular polygons with large perimeter-to-area ratio
  T. Keleti asked, whether the ratio of the perimeter and the area of a finite union of unit squares is always at most 4. In this paper we present an example where the ratio is greater than 4. We also answer the analogous question for regular triangles negatively and list a number of open problems. 
Viktor Kiss, Zolt\'an Vidny\'anszky
math.MG