Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,4,51}

Atlas Canonical Name {2,2,4,51}*1632

Overview

Group
SmallGroup(1632,1200)
Rank
5
Schläfli Type
{2,2,4,51}
Vertices, edges, …
2, 2, 4, 102, 51
Order of s0s1s2s3s4
102
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

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