Looking at some interesting lattices like $E_8$ and the Leech lattice, I was thinking these are all made of 0D objects. Would there be an equivalent object made of 1D or even nD objects.
One might imagine say in 3 dimensions an infinite set of lines arranged in a symmetrical manner such that no line is within a certain distance of another line. Or in higher dimensions a set of infinite planes.
In fact, taking $E_8$ could one join up sets of points with infinite lines to create such an object?
What would these objects be called?
One could imagine that their use would be to find packings of infinite cylinders in higher dimensions instead of the usual spheres.
What you are after is just the cartesian product of some $n$-dimensional lattice with an $m$-dimensional hyperspace, living then within an $(n+m)$-dimensional embedding hyperspace.
--- rk