Merging Edge Geometry

I have a few meshes that are split by faces, this cannot be avoided. So take this cube as an example

I want to show edges so planned on using EdgesGeometry. Since it is not a single mesh, but rather a lot of meshes I will end up with edges duplicated. So the highlighted edge, there would be two, one on top of the other, on for face A and once for face B. This would occur all over. Is there a way to merge all the edges into a single mesh removing the duplicates?

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