Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1632,1200)
Rank
5
Schläfli Type
{51,4,2,2}
Vertices, edges, …
51, 102, 4, 2, 2
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 := ( 2, 3)( 5,65)( 6,67)( 7,66)( 8,68)( 9,61)(10,63)(11,62)(12,64)(13,57)(14,59)(15,58)(16,60)(17,53)(18,55)(19,54)(20,56)(21,49)(22,51)(23,50)(24,52)(25,45)(26,47)(27,46)(28,48)(29,41)(30,43)(31,42)(32,44)(33,37)(34,39)(35,38)(36,40);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,65)(10,66)(11,68)(12,67)(13,61)(14,62)(15,64)(16,63)(17,57)(18,58)(19,60)(20,59)(21,53)(22,54)(23,56)(24,55)(25,49)(26,50)(27,52)(28,51)(29,45)(30,46)(31,48)(32,47)(33,41)(34,42)(35,44)(36,43)(39,40);;
s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67);;
s3 := (69,70);;
s4 := (71,72);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(72)!( 2, 3)( 5,65)( 6,67)( 7,66)( 8,68)( 9,61)(10,63)(11,62)(12,64)(13,57)(14,59)(15,58)(16,60)(17,53)(18,55)(19,54)(20,56)(21,49)(22,51)(23,50)(24,52)(25,45)(26,47)(27,46)(28,48)(29,41)(30,43)(31,42)(32,44)(33,37)(34,39)(35,38)(36,40);
s1 := Sym(72)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,65)(10,66)(11,68)(12,67)(13,61)(14,62)(15,64)(16,63)(17,57)(18,58)(19,60)(20,59)(21,53)(22,54)(23,56)(24,55)(25,49)(26,50)(27,52)(28,51)(29,45)(30,46)(31,48)(32,47)(33,41)(34,42)(35,44)(36,43)(39,40);
s2 := Sym(72)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67);
s3 := Sym(72)!(69,70);
s4 := Sym(72)!(71,72);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;