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In this link, I have drawn a very imprecise figure of a 3D projection of two perpendicular cubes meeting at one of their faces. I have been recently trying to make use of projections to visualise 4D after I realised certain things. I realised that we infer 3D by the difference in shading of a 2D projection. I tried to visualise this particular dichoral angle by imagining the volume of the cubes coloured green, light near the faces and dark at the ends, analogous to the way we might see a dihedral angle between two squares projected on a plane. But as I start trying to infer the fourth dimension from this, I fail somewhere. Otherwise I should be seeing the squares on top to be perpendicular to each other.