Which regular polygons can be dissected into isosceles triangles by non-intersecting diagonals?

Here's one:  a square, one diagonal splits the square into 2 isosceles triangles.

Does this mean a hexagon with diagonals connecting A to C, C to E, and E to A would not qualify?  In this case the diagonals don't cross each other but they do touch each other.  So then they aren't non-intersecting?  So no vertex can have more than one chord coming out of it?

Does each point inside the dissected polygon have to belong to an isosceles triangle (I assume 'yes'), or can some of the area be other shapes?

Posted by Larry on 2012-01-20 23:18:38