World with dodecahedron-shaped trees

Premise

I was inspired by Karl Niklas who used computer modeling to simulate the ideal structure for a tree when different traits were favored. Here is a chart summarizing his work:

Explanation

• L (light): horizontal branches
• M (mechanical stability): fewer horizontal branches
• R (reproduction): taller to spread seeds further

When he combined them all, his model yielded trees that closely resemble trees in the real world, with enough of each trait to survive and reproduce.

A new tree shape

From this point I wanted to take things to a more extreme angle. I want to have trees that are shaped like a dodecahedron:

Question

If we take the point from Niklas' research that trees take a shape that helps them best survive given what the environment deems favorable traits, then what kind of a world do I need for a dodecahedron tree to be deemed favorable?

Further Clarifications:

• Roots: as pictured
• Foliage: configurable
• World: configurable (Earth-like or non-Earth like), we just assume no matter what the world, evolutionary theory, as we understand it, holds to a reasonable degree