The conditions for planerity of comaximal ideal graph with 4 maximal ideals never hold

Question

There is proof for the claim that there is no comaximal ideal graph Which contain 4 maximal ideals and also planer which is definitely true. But some where else I saw an if and only if condition for a comaximal ideal graphs with 4 maximal ideals to be planer. So now i'm try ing to show that conditions never hold. But i got stuck... First defined: Mi=the set of all ideals including mi which are contained in The maximal ideal mi. Vi=Mi - (union on Mj) where i is not the same as j. Vij=(intersection of Mi and Mj)-Mk Where k is not equal to i or j. The conditions are: Vi=1 Or There exist only one Vi with cardinality 2 and Vjk and Vjkl are equal to null for distinct i, j,k