Talk:Crosspolytope
WikiProject Mathematics  (Rated Startclass, Lowimportance)  


WikiProject Uniform Polytopes  

Contents
Can someone add a hendecacross (11orthoplex)?
I need someone to add it because I would like to see what it looks like. LittleWhole (talk) 00:46, 29 November 2016 (UTC)
 Why stop at 11? All you need to do is draw a regular 22gon, and connect all pairs of vertices, except opposite ones. Tom Ruen (talk) 04:30, 29 November 2016 (UTC)
Tessellation
Can someone tell me how many 16cells (how many polychlora), how many facets (how many tetrahedra), how many ridges (how many triangular faces), and how many edges meet at any given vertex in a tessellation of regular 16cells in Euclidean 4space? (Untitled/unsigned question from Kevin Lamoreau 9 August 2005, belatedly moved into a properly titled section so it can be answered cleanly)
 Probably 16cell honeycomb would have been a better place to ask. But in case you're still monitoring this, nearly 10 years after having asked, let's close this out. You're asking about the kfaces incident to a single vertex of {3,3,4,3}; the dual question, with the same answers, asks about the (4k)faces incident to a single polychoron of {3,4,3,3}. I.e., "How many vertices, edges, faces, cells does a 24cell have?" The answers are 24, 96, 96, 24, respectively. Joule36e5 (talk) 03:56, 23 June 2015 (UTC)
sources?
I mostly added the resource template because I'd like sources for this name. Tom Ruen 00:54, 29 July 2006 (UTC)
Names in higher dimensions
Where did all these teron, peton, etc. names come from? Who first called them that? I'm a little suspicious because triacontaditeron, for example, gets zero Google hits. —Keenan Pepper 04:37, 4 September 2006 (UTC)
 See reply under Talk:Simplex. Search for polyteron' or triacontadi. No google hits for triacontadigon either, but it is a common 32gon. Tom Ruen 04:55, 4 September 2006 (UTC)
 Actually a 32gon is a dotriacontagon or better yet a triacontakaidigon. —Keenan Pepper 05:22, 4 September 2006 (UTC)
Higher dimensions
Without warning, the author appears to have reverted to the secondary, parenthetical definition of a crosspolytope  i.e. "(... [S]ome authors define a crosspolytope only as the boundary of this region.)". For the formula to be valid, k is restricted to values less than n. (Even if k=n is used, since 1/(1)! = 0, the formula gives zero rather than one needed the number of ndimensional components in an ncross if the primary definition is used.) For consistency with the simplex and hypercube articles, the value 1 should be in table locations where k=n. Also for consistency with other dimensions and the hypercube article, shouldn't the graph for a onedimensional crosspolytope include its single edge (Complete_graph_K2.svg)? I will add a similar question on the simplex article. 24.6.65.170 (talk) 16:46, 13 July 2009 (UTC)
Numbers of components for arbitrary n dimensions
After a row for each dimension n and a specific count for each column by dimension k of the component, the table ends on a last row with a single formula in k and n which isn't that easy to specialize to specific values of k. IOW, an intermediary row populating each column k with a corresponding simplified formula in n would be in style.
83.76.122.54 (talk) 11:58, 31 March 2012 (UTC)