@gsuberland initially I had discarded these because two triangles that shared two vertices could not overlap since either they are both facing the camera or backface culling would have removed one of them from the mesh before the hidden wireframe stage.
@th Wasn't the trick to sort the points vertically, then work downwards spitting out 'quads' as you end a triangle?
@th additional one: scalene sharing two vertices of an equilateral, but poking out the side.