# Talk:Runcinated 5-simplexes

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## Element count for Runcitruncated 5-simplex

Polymake, analyzing a polytope with the given coordinates for the Runcitruncated 5-simplex, finds different element counts: 630 edges, 720 2-faces, and 315 3-faces. Since the currently listed counts (540 edges, 570 2-faces, 255 3-faces) are the same as for the runcicantellated 5-simplex below it, I think they're probably an error, so I've changed them. (Also, the given vertex-figure implies there should be 180*7/2 = 630 edges.) --kundor (talk) 15:03, 25 July 2013 (UTC)

Kundor, thanks for checking! Klitzing webpage has the polytopes under the Bower names, here [1], linked from [2]. The diagonals of the matrix represents element counts by positions in the fundamental simplex, so you have to hand-count them, shows 180 vertices, 630 edges, 720 faces, 315 cells, 47 4-faces, consistent with your count. So I can't say where the wrong numbers came from, but again, glad you're checking! Someday the stat table should also be updated with complete face and cell types listing, which Klitzing lists with diamond links by row. Tom Ruen (talk) 20:08, 25 July 2013 (UTC)
P.s. To avoid errors, I've considered moving stat tables to template databases, like you can see at Rectified 5-simplex (http://en.wikipedia.org/w/index.php?title=Rectified_5-simplex&action=edit&section=1), and Template:Uniform_polyteron_db, tested on only 3 polytopes. So such a file can be created say from a spreadsheet, and easy for simple counts, more work to list all the element types. Tom Ruen (talk) 20:21, 25 July 2013 (UTC)