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In Hasse Diagrams of divisibility am I allowed to cross edges? If so then I believe I have a solution, if not then here's where my problem lies.

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See this for an algorithm to draw hasse diagrams for finite posets. – Git Gud Nov 27 '13 at 23:00
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Yes, you can create a Hasse Diagram. Any finite poset can be made into a Hasse diagram, and your set ordered by divisibility forms a poset. There is also no requirement for Hasse diagrams to be planar, or else the most common examples of posets, such as $B_n$ for $n > 2$ would not be "diagrammable".

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Yes -- there's no requirement that a Hasse diagram has to be planar.

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