Three regular polygons, all with unit sides, share a common vertex and are all coplanar. Each polygon has a different number of sides, and each polygon shares a side with the other two; there are no gaps or overlaps. Find the number of sides for each polygon. There are multiple answers.

to meet the requirements, the sum of the inside angles of
the polygons should be 180 degrees. i've found four com-
binations that i believe will work.

-square: 90 (degrees of inner angle)
-hexagon: 120
-12 sided: 150 (is that called a dodecagon?)

-triangle: 60
-9 sided: 140
-18 sided: 160

-triangle: 60
-octagon: 135
-24 sided: 165

-square: 90
-pentagon: 108
-20 sided: 162

there are more combinations. i'll post if i find any.

Posted by rixar on 2004-07-12 19:26:03