A325176 Numbers k such that an Archimedean 4-polytope with k vertices exists.

5, 8, 10, 16, 20, 24, 30, 32, 48, 60, 64, 96, 100, 120, 144, 192, 288, 384, 576, 600, 720, 1152, 1200, 1440, 2400, 3600, 7200, 14400

Offset

1,1

Comments

Also, numbers n such that a Catalan 4-polytope (dual of an Archimedean 4-polytope) with n cells (3-D facets) exists.

References

J. H. Conway, H. Burgiel and Chaim Goodman-Strauss, The Symmetries of Things, A K Peters, Ltd., 2008, pp. 389-403, ISBN 978-1-56881-220-5.

Links

Table of n, a(n) for n=1..28.

Marco Möller, 4-dimensionale Archimedische Polytope, Results in Mathematics, Vol. 46, No. 3-4 (2004), 271-360 (in German) [Subscription required].

Marco Möller, 4-dimensionale Archimedische Polytope, Dissertation, Universität Hamburg, 2004 (in German).

Wikipedia, Schläfli symbol - Polychora and honeycombs

Wikipedia, Uniform 4-polytope

Example

Vertices |  Example 4-polytope
         |  (Schläfli symbol)
----------------------------------------
      5  | {3,3,3}
      8  | {3,3,4}
     10  | r{3,3,3}
     16  | {4,3,3}
     20  | t{3,3,3}
     24  | {3,4,3}
     30  | rr{3,3,3}
     32  | r{4,3,3}
     48  | t{3,3,4}
     60  | tr{3,3,3}
     64  | t{4,3,3}
     96  | rr{4,3,3}
    100  | grand antiprism
    120  | {3,3,5}
    144  | t_0,3{3,4,3}
    192  | t{3,4,3}
    288  | rr{3,4,3}
    384  | t_0,1,2,3{3,3,4}
    576  | tr{3,4,3}
    600  | {5,3,3}
    720  | r{3,3,5}
   1152  | t_0,1,2,3{3,4,3}
   1200  | r{5,3,3}
   1440  | t{3,3,5}
   2400  | t{5,3,3}
   3600  | rr{5,3,3}
   7200  | tr{5,3,3}
  14400  | t_0,1,2,3{5,3,3}

Crossrefs

Cf. A092538.

Sequence in context: A329237 A314384 A196384 * A164682 A157482 A314385

Adjacent sequences: A325173 A325174 A325175 * A325177 A325178 A325179

Keyword

nonn,fini,full

Author

Felix Fröhlich, Sep 05 2019

Status

approved