2,1

Hugo Pfoertner, Intersections of diagonals in polygons of triangular shape.

Sequences formed by drawing all diagonals in regular polygon

a(2)=12 because the 6 line segments mutually connecting the vertices and the mid-side nodes form 12 congruent right triangles of two different sizes.

a(3)=75: 48 triangles, 24 quadrilaterals and 3 pentagons are formed. See pictures at Pfoertner link.

Cf. A092866 Number of intersections, A092098 regions in triangle cut by line segments connecting vertices with subdivision points on opposite side, A006533 regions formed by all diagonals in regular n-gon, A002717 triangles in triangular matchstick arrangement.

Sequence in context: A064121 A064116 A003368 this_sequence A053310 A006235 A009642

Adjacent sequences: A092864 A092865 A092866 this_sequence A092868 A092869 A092870

more,nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 15 2004