Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,4,57}

Atlas Canonical Name {2,2,4,57}*1824

Overview

Group
SmallGroup(1824,1247)
Rank
5
Schläfli Type
{2,2,4,57}
Vertices, edges, …
2, 2, 4, 114, 57
Order of s0s1s2s3s4
114
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

19-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80);;
s3 := ( 6, 7)( 9,77)(10,79)(11,78)(12,80)(13,73)(14,75)(15,74)(16,76)(17,69)(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,61)(26,63)(27,62)(28,64)(29,57)(30,59)(31,58)(32,60)(33,53)(34,55)(35,54)(36,56)(37,49)(38,51)(39,50)(40,52)(41,45)(42,47)(43,46)(44,48);;
s4 := ( 5, 9)( 6,12)( 7,11)( 8,10)(13,77)(14,80)(15,79)(16,78)(17,73)(18,76)(19,75)(20,74)(21,69)(22,72)(23,71)(24,70)(25,65)(26,68)(27,67)(28,66)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)(36,58)(37,53)(38,56)(39,55)(40,54)(41,49)(42,52)(43,51)(44,50)(46,48);;
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*s1*s0*s1, 
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(80)!(1,2);
s1 := Sym(80)!(3,4);
s2 := Sym(80)!( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80);
s3 := Sym(80)!( 6, 7)( 9,77)(10,79)(11,78)(12,80)(13,73)(14,75)(15,74)(16,76)(17,69)(18,71)(19,70)(20,72)(21,65)(22,67)(23,66)(24,68)(25,61)(26,63)(27,62)(28,64)(29,57)(30,59)(31,58)(32,60)(33,53)(34,55)(35,54)(36,56)(37,49)(38,51)(39,50)(40,52)(41,45)(42,47)(43,46)(44,48);
s4 := Sym(80)!( 5, 9)( 6,12)( 7,11)( 8,10)(13,77)(14,80)(15,79)(16,78)(17,73)(18,76)(19,75)(20,74)(21,69)(22,72)(23,71)(24,70)(25,65)(26,68)(27,67)(28,66)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)(36,58)(37,53)(38,56)(39,55)(40,54)(41,49)(42,52)(43,51)(44,50)(46,48);
poly := sub<Sym(80)|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*s1*s0*s1, 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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;