# Talk:Waterman polyhedron

I think the pyramidal symmetries are wrong, please correct Vel (talk) 08:11, 24 March 2023 (UTC)

That given definition of Waterman polyhedra is **completely wrong**, it rather is much, much more general! -
It is meant to use *any* possible lattice, and to use *any* symmetric center point therein (i.e. a lattice point, but also a (deep, shallow, ...) hole would be allowed as well). (Non-symmetric center points could be considered likewise, but would lead to non-interesting, asymmetrical polyhedra instead.)
Then the polyhedron gets defined as the hull of those lattice points which are contained within a sphere of a given radius around that center point.
This setup in November 2006 was introduced by Steve Waterman and then elaborated in full in the community of the Polyhedron Maillist Archive.
Note that this setup further extends likewise to *any* dimension as well.
Klitzing 10:38, 26 March 2023 (CET)