Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,16,6}

Atlas Canonical Name {5,2,16,6}*1920

Overview

Group
SmallGroup(1920,203901)
Rank
5
Schläfli Type
{5,2,16,6}
Vertices, edges, …
5, 5, 16, 48, 6
Order of s0s1s2s3s4
240
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (12,15)(13,16)(14,17)(18,24)(19,25)(20,26)(21,27)(22,28)(23,29)(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,42)(37,43)(38,44)(39,45)(40,46)(41,47);;
s3 := ( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,39)(13,41)(14,40)(15,36)(16,38)(17,37)(18,48)(19,50)(20,49)(21,51)(22,53)(23,52)(24,42)(25,44)(26,43)(27,45)(28,47)(29,46);;
s4 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(53)!(2,3)(4,5);
s1 := Sym(53)!(1,2)(3,4);
s2 := Sym(53)!(12,15)(13,16)(14,17)(18,24)(19,25)(20,26)(21,27)(22,28)(23,29)(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,42)(37,43)(38,44)(39,45)(40,46)(41,47);
s3 := Sym(53)!( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,39)(13,41)(14,40)(15,36)(16,38)(17,37)(18,48)(19,50)(20,49)(21,51)(22,53)(23,52)(24,42)(25,44)(26,43)(27,45)(28,47)(29,46);
s4 := Sym(53)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52);
poly := sub<Sym(53)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;