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%I #14 Mar 08 2019 23:59:00
%S 120,720,1200,120,120,1200,720,120,120,720,720,120,120,720,720,120,
%T 120,720,720,120,120,720,720,120,120,720,1200,120,120,1200,720,120,
%U 120,720,1200,600,600,1200,720,120
%N Number of elements in the ten nonconvex regular 4-polytopes (regular 4-dimensional star-polytopes), as a four-column array, read by rows, with rows ordered first by increasing density, then by increasing cell-count, then by increasing face-count, then by increasing edge-count and then by increasing vertex-count.
%C Only included for completeness (see other sequences in crossrefs). This is one of those entries that I think should be included since it is such an elementary sequence in geometry, but where the terms do otherwise not really make a very spectacular sequence.
%C The ordering of the polytopes in the enumeration of the element counts is somewhat arbitrary, though based on invariants inherently associated with these polytopes. For example, ordering first by vertex-count, then by edge-count, then by face-count and then by cell-count might have been as good a choice as the one used for the sequence.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_4-polytope#Regular_star_.28Schl.C3.A4fli.E2.80.93Hess.29_4-polytopes">Regular 4-polytope - Regular star (Schläfli-Hess) 4-polytopes</a>
%e Polytope | Schläfli symbol | Density | Cells | Faces | Edges | Vertices
%e ----------------------------------------------------------------------------------
%e Sm st 120-cell | {5/2,5,3} | 4 | 120 | 720 | 1200 | 120
%e Ico 120-cell | {3,5,5/2} | 4 | 120 | 1200 | 720 | 120
%e Grt 120-cell | {5,5/2,5} | 6 | 120 | 720 | 720 | 120
%e Grd 120-cell | {5,3,5/2} | 20 | 120 | 720 | 720 | 120
%e Grt st 120-cell | {5/2,3,5} | 20 | 120 | 720 | 720 | 120
%e Grd st 120-cell | {5/2,5,5/2} | 66 | 120 | 720 | 720 | 120
%e Grt grd 120-cell | {5,5/2,3} | 76 | 120 | 720 | 1200 | 120
%e Grt ico 120-cell | {3,5/2,5} | 76 | 120 | 1200 | 720 | 120
%e Grt grd st 120-cell | {5/2,3,3} | 191 | 120 | 720 | 1200 | 600
%e Grd 600-cell | {3,3,5/2} | 191 | 600 | 1200 | 720 | 120
%e ======================
%e | Keys |
%e ======================
%e | Sm | Small |
%e | St | Stellated |
%e | Grt | Great |
%e | Grd | Grand |
%e | Ico | Icosahedral |
%e ======================
%Y Cf. A048789, A063924, A063925, A063926, A063927.
%K nonn,tabf,fini,full
%O 1,1
%A _Felix Fröhlich_, Feb 27 2019
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