Part of the Atlas of Small Regular Polytopes

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

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

Overview

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