Draw a specific graph with a branching.

Question

I want to draw the following graph:

1. it is a tree
2. it can have up to four children nodes
3. there should be no edges intersections

The part with which I struggle is the 3. I am not sure how to avoid the intersections.

Whatever distance I will take between sibling nodes eventually an intersection will occur if I will add four children to each node enough times.

Is it possible to accomplish at all?

I am going to draw the graph programmatically.