Hello. I have the problem that i want to model a building with blender. I have multiple wall tiles wich i want to combine. For the corner i have the following problem (see screenshot)
I want to connect bot sides together but i dont want to extrude one site. Is there a tool that allows to create an single vertex to create an face ?
Welcome 
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If you delete the inner edge and use the F2 addon on the rectangular point of the triangle then it will add a quad based on this side edges…
You can actually extrude the face without destroying your geometry:
Press E then right click to cancel.
Press ALT + E and choose Extrude Manifold. You can use Snap to Vertex.
Press H to hide the face. Select and delete the inner face.
Press ALT + H to unhide.
Takes less time than the manual approach.
But maybe you actually need a vertex at the intersection of two edges in the future. For that, you can use the TinyCAD add-on. It comes with Blender.
Just select two edges, right click, TinyCAD, Vertex at Intersection.
Or you can also choose AUTO. The edges are automatically extended to the intersection point.
