Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,57}

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

Overview

Group
SmallGroup(1824,1245)
Rank
4
Schläfli Type
{2,6,57}
Vertices, edges, …
2, 8, 228, 76
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)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45)(48,49)(52,53)(56,57)(60,61)(64,65)(68,69)(72,73)(76,77);;
s2 := ( 5, 6)( 7,75)( 8,76)( 9,78)(10,77)(11,71)(12,72)(13,74)(14,73)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,59)(24,60)(25,62)(26,61)(27,55)(28,56)(29,58)(30,57)(31,51)(32,52)(33,54)(34,53)(35,47)(36,48)(37,50)(38,49)(39,43)(40,44)(41,46)(42,45);;
s3 := ( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,78)(12,76)(13,77)(14,75)(15,74)(16,72)(17,73)(18,71)(19,70)(20,68)(21,69)(22,67)(23,66)(24,64)(25,65)(26,63)(27,62)(28,60)(29,61)(30,59)(31,58)(32,56)(33,57)(34,55)(35,54)(36,52)(37,53)(38,51)(39,50)(40,48)(41,49)(42,47)(43,46);;
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*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*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*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45)(48,49)(52,53)(56,57)(60,61)(64,65)(68,69)(72,73)(76,77);
s2 := Sym(78)!( 5, 6)( 7,75)( 8,76)( 9,78)(10,77)(11,71)(12,72)(13,74)(14,73)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,59)(24,60)(25,62)(26,61)(27,55)(28,56)(29,58)(30,57)(31,51)(32,52)(33,54)(34,53)(35,47)(36,48)(37,50)(38,49)(39,43)(40,44)(41,46)(42,45);
s3 := Sym(78)!( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,78)(12,76)(13,77)(14,75)(15,74)(16,72)(17,73)(18,71)(19,70)(20,68)(21,69)(22,67)(23,66)(24,64)(25,65)(26,63)(27,62)(28,60)(29,61)(30,59)(31,58)(32,56)(33,57)(34,55)(35,54)(36,52)(37,53)(38,51)(39,50)(40,48)(41,49)(42,47)(43,46);
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*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*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*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s1*s2 >;