'Pinching' corners of a Mesh

I am trying to pinch corners on a mesh, and also having the faces touch as if they were to be attached at the point shown on the photo.

I am able to get them to overlap (which is what I need) but not touch face to face without intersecting. I have added 3 anchor points, two where the corners should be and another at the point were they ‘connect’ - but this just causes an intersection rather than face to face.

Any ideas how I can do this??