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A306602 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. 0
120, 720, 1200, 120, 120, 1200, 720, 120, 120, 720, 720, 120, 120, 720, 720, 120, 120, 720, 720, 120, 120, 720, 720, 120, 120, 720, 1200, 120, 120, 1200, 720, 120, 120, 720, 1200, 600, 600, 1200, 720, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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.

LINKS

Table of n, a(n) for n=1..40.

Wikipedia, Regular 4-polytope - Regular star (Schläfli-Hess) 4-polytopes

EXAMPLE

Polytope            | Schläfli symbol | Density | Cells | Faces | Edges | Vertices

----------------------------------------------------------------------------------

Sm st 120-cell      | {5/2,5,3}       |       4 |   120 |   720 |  1200 |      120

Ico 120-cell        | {3,5,5/2}       |       4 |   120 |  1200 |   720 |      120

Grt 120-cell        | {5,5/2,5}       |       6 |   120 |   720 |   720 |      120

Grd 120-cell        | {5,3,5/2}       |      20 |   120 |   720 |   720 |      120

Grt st 120-cell     | {5/2,3,5}       |      20 |   120 |   720 |   720 |      120

Grd st 120-cell     | {5/2,5,5/2}     |      66 |   120 |   720 |   720 |      120

Grt grd 120-cell    | {5,5/2,3}       |      76 |   120 |   720 |  1200 |      120

Grt ico 120-cell    | {3,5/2,5}       |      76 |   120 |  1200 |   720 |      120

Grt grd st 120-cell | {5/2,3,3}       |     191 |   120 |   720 |  1200 |      600

Grd 600-cell        | {3,3,5/2}       |     191 |   600 |  1200 |   720 |      120

======================

| Keys               |

======================

| Sm   | Small       |

| St   | Stellated   |

| Grt  | Great       |

| Grd  | Grand       |

| Ico  | Icosahedral |

======================

CROSSREFS

Cf. A048789, A063924, A063925, A063926, A063927.

Sequence in context: A069085 A039688 A005820 * A300299 A052787 A292970

Adjacent sequences:  A306599 A306600 A306601 * A306603 A306604 A306605

KEYWORD

nonn,tabf,fini,full

AUTHOR

Felix Fröhlich, Feb 27 2019

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)