Is this twisted cube like graph planar?

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I couldn't find any planar representation of this graph neither could I find a subdivision or minor of $K_{5}$ or $K_{3,3}$. So I don't know how to go about it. Please help.

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If you contract the two long vertical edges, you are left with $K_{3,3}$ So $K_{3,3}$ is a minor of your graph, which is in turn not planar.

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