Ninety non-intersecting slats on six axes with icosahedral symmetry.
Inspired by John Kostik’s 6 axis 15 vZome model, I attempted to duplicate the model shown in this YouTube video.
I discovered that the trick to rotating a 30-gon prism centered the blue Z axis onto a golden field’s red icosahedral axis of symmetry is to construct a mirror tool on the plane that bisects the blue and red axes and is perpendicular to the plane formed by them. After constructing such a mirror tool, a prism can be built as usual on the blue Z axis, then it is mirrored (moved, not copied) onto the red axis and then tetrahedral symmetry is applied to it. The result is a set of 6 prisms, each on one of the 6 axes of icosahedral symmetry even though the vZome 30-gon field does not (yet) support icosahedral symmetry.
I chose the 30-gon field to match the design in the YouTube video, but this general technique of applying a mirror can conceptually be applied to any 10N-gon field. It can not be applied to odd 5N-gon fields because the antiprism symmetry in those fields uses embedding, but the red axis from icosahedral symmetry does not.