For the problem as stated, there are six sets of polygons:
3, 7, 42
3, 8, 24
3, 9, 18
3, 10, 15
4, 5, 20
4, 6, 12
If you extend the problem and ask for any number of any polygon at the vertex, the list is as follows:
3 hexagons;
2 pentagons; 1 10-gon;
1 square; 2 8-gons;
1 square; 1 hexagon; 1 12-gon;
1 square; 1 pentagon; 1 20-gon;
4 squares;
1 triangle; 2 12-gons;
1 triangle; 1 7-gon; 1 42-gon;
1 triangle; 1 8-gon; 1 24-gon;
1 triangle; 1 9-gon; 1 18-gon;
1 triangle; 1 10-gon; 1 15-gon;
1 triangle; 2 squares; 1 hexagon;
2 triangles; 2 hexagons;
2 triangles; 1 square; 1 12-gon;
3 triangles; 2 squares;
4 triangles; 1 hexagon;
6 triangles;
Charlie produced this result using a program here and a correction here. |
