Talk:Zonohedron

Zonotope vs. zonohedron

In my opinion, the notion of a zonotope is more important in mathematics (convex geometry) than is its special case, the zonohedron (=zonotope in 3D). Therefore, the facts about zonotopes, mentioned in the this article should be moved to a separate one and appropriate links should be set. Nysgerrig (talk) 19:41, 3 October 2010 (UTC)

I agree. In my opinion a page for zonoids (a generalization of zonotopes) should be created. I would like to do it but have never created a Wikipedia page before. If anyone is interested, let me know. Leoleleoleo (talk) 09:24, 23 August 2024 (UTC)

Question

Given a zonotope defined by k vectors in n dimensional space (k>=n), is there an algorithm for determining if point p is inside the zonotope?

Sure. It's an example of a linear programming feasibility problem with equality constraints: p is in the zonotope iff there exist x_i, 0≤x_i≤1, s.t. p = Σx_iv_i. So any linear programming algorithm will solve it. —David Eppstein 07:23, 7 September 2006 (UTC)

Dimension?

I don't know what the just added dimension column means. Tom Ruen 21:25, 23 May 2007 (UTC)

Hypercube

"Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional projection of a hypercube."

This is flat-out wrong. While various three dimensional projections of a hypercube are zonohedra, not all zonohedra are. With respec to these things being equivalent, this is only the case when the zonohedron is the sum of four line segments, and there are probably addittional restrictions on how those line segments are oriented if they are to be the projections of the edges of the axes of a hypercube. —Preceding unsigned comment added by 124.178.225.104 (talk) 14:58, 4 December 2010 (UTC)

"Hypercube" does not necessarily mean "four-dimensional hypercube". A zonohedron with k generators is the projection of a k-dimensional hypercube. —David Eppstein (talk) 17:11, 4 December 2010 (UTC)

Generators

Apart from http://www.ics.uci.edu/~eppstein/junkyard/ukraine/ukraine.html, there is no comprehensive list of the generators for the zonohedrons in this article, at least that I know of. Should not this article or the Wikipedia articles on the individual zonohedrons specify the generator set? — Preceding unsigned comment added by Decatur-en (talk • contribs) 18:15, 24 May 2012 (UTC)

Zonohedra that fill space

The section begins: "The original motivation for studying zonohedra is that the Voronoi diagram of any lattice forms a convex uniform honeycomb in which the cells are zonohedra." The Voroni cell of the diamond lattice (or "Triakis truncated tetrahedral honeycomb" as mathematicians call it) is a Triakis truncated tetrahedron, which I am pretty sure is not a zonohedron. As I am not a mathematician, I am not sure I should edit the main article. Pciszek (talk) 20:29, 24 April 2020 (UTC)

The diamond lattice is also not a lattice in the technical sense used here. —David Eppstein (talk) 20:45, 24 April 2020 (UTC)