Talk:Centered polyhedral number

… surrounded by polyhedral layers with a constant number of edges
First of all, the article has to define a polyhedral layer. Otherwise I’d prefer to see it redirected or de-articled in some other way. Incnis Mrsi (talk) 16:49, 28 July 2013 (UTC)
 * I agree that this could perhaps be formulated in a more understandable way. A polyhedral layer here is a set of points all lying on the edges of the defining polyhedron. --  Toshio   Yamaguchi  20:18, 28 July 2013 (UTC)
 * Really on the edges only? How can you explain a cubic growth of centered tetrahedral numbers then? Incnis Mrsi (talk) 20:47, 28 July 2013 (UTC)
 * You are correct, it is not the edges only. For example, the the fourth centered tetrahedral number is 35, because there is a central point, a layer with 4 points, a layer with 10 points and a layer with 20 points. In the layer with 20 points, there are 4 points lying at the center of the faces of the tetrahedron.


 * I think a face of the layer with 20 points looks like this:

x  x x  x x x x x x x
 * In each additional layer, a new row of Xs (points) is added at the bottom of the triangle, containing one point more than the row above it. So the correct formulation probably should have been A polyhedral layer is the set of all points forming the surface of the tetrahedron. --  Toshio   Yamaguchi  22:32, 28 July 2013 (UTC)