How to delete faces that intersect an edge with geometry nodes?

I have the following mesh:

And I'm instancing cubes on every vertex like this:

Consider that each vertex can only connect to 6 edges (up, down, left, right, forward, backwards), is there a way to delete the faces that intersect the original edges?

What I have attempted:

• In all attempts I tried using the Edge Vertices node, by subtracting position 1 from position 2 to get the edge direction.
• I tried to use this edge direction to compare with the dot product of the face normal, but that didn't work correctly (some faces disappear, but not the ones I want)
• I also tried to use the edge direction to raycast from the center of the cube instances, but that didn't work either (same as above)

This was my latest attempt: