I have tried to construct as magic as possible 9x9x9x9 magic hypercubes.

Firstly I have constructed a pantriagonal 9x9x9x9 magic hypercube which is panmagic in the levels, 3x3 compact in the levels, symmetric and 50% panquadrogonal magic.

Secondly I have constructed a panquadrogonal 9x9x9x9 magic hypercube which is 3x3 compact in the levels, symmetric, each 1/3 row/column/pillar/post gives 1/3 of the magic sum and the hypercube is more than 50% pantriagonal magic.