How to Create Perfect Edges While Designing Shapes

Hello!

Recently I was creating a low poly-esque background using the polygon tool and the distort filter. It turned out alright, but being imperfect when drawing the triangles often leads to stuff like this happening (zoomed in screenshot):

Is there a way to create seamless shapes? And if not, what is the easiest way to fix this? Both the obvious border between the shapes and the overlapped point.

Thank you so much for the help!