Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,57,6}

Atlas Canonical Name {2,57,6}*1824

Overview

Group
SmallGroup(1824,1245)
Rank
4
Schläfli Type
{2,57,6}
Vertices, edges, …
2, 76, 228, 8
Order of s0s1s2s3
76
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

12-fold

19-fold

38-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 5)( 7,75)( 8,77)( 9,76)(10,78)(11,71)(12,73)(13,72)(14,74)(15,67)(16,69)(17,68)(18,70)(19,63)(20,65)(21,64)(22,66)(23,59)(24,61)(25,60)(26,62)(27,55)(28,57)(29,56)(30,58)(31,51)(32,53)(33,52)(34,54)(35,47)(36,49)(37,48)(38,50)(39,43)(40,45)(41,44)(42,46);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,75)(12,76)(13,78)(14,77)(15,71)(16,72)(17,74)(18,73)(19,67)(20,68)(21,70)(22,69)(23,63)(24,64)(25,66)(26,65)(27,59)(28,60)(29,62)(30,61)(31,55)(32,56)(33,58)(34,57)(35,51)(36,52)(37,54)(38,53)(39,47)(40,48)(41,50)(42,49)(45,46);;
s3 := ( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)(39,42)(43,46)(47,50)(51,54)(55,58)(59,62)(63,66)(67,70)(71,74)(75,78);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 4, 5)( 7,75)( 8,77)( 9,76)(10,78)(11,71)(12,73)(13,72)(14,74)(15,67)(16,69)(17,68)(18,70)(19,63)(20,65)(21,64)(22,66)(23,59)(24,61)(25,60)(26,62)(27,55)(28,57)(29,56)(30,58)(31,51)(32,53)(33,52)(34,54)(35,47)(36,49)(37,48)(38,50)(39,43)(40,45)(41,44)(42,46);
s2 := Sym(78)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,75)(12,76)(13,78)(14,77)(15,71)(16,72)(17,74)(18,73)(19,67)(20,68)(21,70)(22,69)(23,63)(24,64)(25,66)(26,65)(27,59)(28,60)(29,62)(30,61)(31,55)(32,56)(33,58)(34,57)(35,51)(36,52)(37,54)(38,53)(39,47)(40,48)(41,50)(42,49)(45,46);
s3 := Sym(78)!( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)(39,42)(43,46)(47,50)(51,54)(55,58)(59,62)(63,66)(67,70)(71,74)(75,78);
poly := sub<Sym(78)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;