How to Construct Irregular Hexagon

Hello, I am trying to construct an irregular hexagon with 3 different vertices; an individual vertex has equal length edges and 120° but the 3 vertices have different edge lengths.  The edge lengths cannot be trimmed so the line ends must snap together.  Wireframe view, zoomed in to the max, shows this is hard to do.  I found a workaround but it requires changing the edge lengths (still equal) of one vertex.  Thanks!