[gtwtrthj] Uniform density branched-chain alkane

Design a highly branched alkane in the shape of a sphere (ball) with approximately constant density of carbon atoms within its interior.

Every carbon in sp3 hybridization (tetrahedron).  Assume bond angles and lengths are exactly constant, like a molecular model.  Bonds can turn, which provide a lot of freedom.   What computational algorithm?

Kind of an extension of methane and neopentane.

Ball of wax