And because why not, here are six Z4 surrounding a cube:
off_align -F z4.off,0,1,0 cube | off_align -F z4.off,4,1,2 | \ off_align -F z4.off,1,1,1 | off_align -F z4.off,2,1,3 | \ off_align -F z4.off,0,1,2 | off_align -F z4.off,0,1,3 | antiview
And then that’s subtracted from six J91 surrounding a cube (essentially) because, yes, six J91 will fit around a cube:
off_align -F J91,1,1,0 z4_6.off | off_util -M b | off_align -F J91,21,1,0 | \ off_util -M b | off_align -F J91,83,1,0 | \ off_util -M b | off_align -F J91,103,1,0 | \ off_util -M b | off_align -F J91,41,1,0 | \ off_util -M b | off_align -F J91,61,1,0 | \ off_util -M b | antiview
So, yeah, a regular faced polyhedron with three mutually perpendicular tunnels passing through its center.