For any point P inside it, the area of A'B'C' is equal to the sum of the areas of the triangles PB'C' , PC'A' and PA'B' PA, PB and PC are the heights of triangles PB'C', PC'A' and PA'B'. Points L, M and N are the midpoints of the sides of A'B'C'. If the point P lies on NM then height PA is half the height of A'B'C' and PA represents exactly half the votes cast for party A'. With seven or more sides there must be two consecutive obtuse angles as there are at most three acute angles. The simplest patterns are 3 and 12 in which the motif is repeated by a translation along the strip.
Translations are the only transformations involved.
This pattern involves half turns and translations. This pattern involves reflections in the horizontal axis and translations. This pattern involves glide reflections in the horizontal axis and translations. This pattern involves reflections in a perpendicular axis and translations. This pattern involves reflections in the horizontal and in a perpendicular axis, half turns and translations.