I have ask this question in math.stackexchange, here. Since, there is no answer and apart from that i feel that the problem is difficult, i would like to ask it here. The problem is to find the genus of $K_{4,2,2,2}$. I want a theoretical technique(if possible), otherwise using sage programming is good enough. I have tried using sage for a week now, but my computer is too slow. Thanks for any help.

The graph $K_{4,2,2,2}$ is a complete $4-$partite graph, that is, its vertex set can be partition into 4 disjoint parts of size 4, 2, 2 and 2, and any two vertices are adjacent if and only if they belong to different parts.

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