Part of the Atlas of Small Regular Polytopes

Polytope of Type {11,2,42}

Atlas Canonical Name {11,2,42}*1848

Overview

Group
SmallGroup(1848,147)
Rank
4
Schläfli Type
{11,2,42}
Vertices, edges, …
11, 11, 42, 42
Order of s0s1s2s3
462
Order of s0s1s2s3s2s1
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

6-fold

7-fold

14-fold

21-fold

Covers minimal covers in bold

None in this atlas.

Representations

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