How to prevent edge lapping in graphviz with circo layout

I was trying to draw a circular graph using GraphViz, and decided it would be the best to use circo for this graph.

Having taken advice in a post from 7 years ago, How to prevent edges in graphviz to overlap each other, and using global overlap=false and splines=true, the edges still overlap with each other.

The whole graph can be seen here, and is defined as:

digraph question6 {

 layout="circo"
 overlap=false
 splines=true
 node [shape="circle"]

 G1 [label="1, G"]
 G2 [label="2, G"]
 D11 [label="1, D1"]
 D12 [label="2, D1"]
 D21 [label="1, D2"]
 D22 [label="2, D2"]

 G1 -> D12 [label="c"]
 G1 -> G2 [label="a"]
 G2 -> D12 [label="a"]
 D11 -> G1 [label="d"]
 D11 -> D21 [label="e"]
 D11 -> D12  [label="c"]
 D12 -> G2 [label="d"]
 D12 -> D22 [label="c"]
 D21 -> G1 [label="d"]
 D21 -> D22 [label="c"]

 D22 -> D21 [label="b"]
 D22 -> G2 [label="d"]
}

Solution

As for now, there is not a viable way for this.

One of the very difficult things that GraphViz is not yet able to resolve is to determine if the graph is planar.