Is there any way to graphically represents the duals of nsimplices? For example, I want to know how exactly duals of tetrahedrons arrange between themselves, i.e how many faces, volumes share the same link... etc
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I'm not sure it meets your request, but I think this is explained in Griffith & Harris, "Principles of Algebraic Geometry", in chapter 0, paragraph on Poincaré duality (page 53 and following pages). 

