Polytope of Type {2,20,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6,2,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,236184)
Rank : 6
Schlafli Type : {2,20,6,2,2}
Number of vertices, edges, etc : 2, 20, 60, 6, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,6,2,2}*960
   3-fold quotients : {2,20,2,2,2}*640
   5-fold quotients : {2,4,6,2,2}*384a
   6-fold quotients : {2,10,2,2,2}*320
   10-fold quotients : {2,2,6,2,2}*192
   12-fold quotients : {2,5,2,2,2}*160
   15-fold quotients : {2,4,2,2,2}*128
   20-fold quotients : {2,2,3,2,2}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)(41,55)
(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);;
s2 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)(12,45)
(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)(23,59)
(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);;
s3 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)(22,27)
(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);;
s4 := (63,64);;
s5 := (65,66);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)
(41,55)(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);
s2 := Sym(66)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)
(12,45)(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)
(23,59)(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);
s3 := Sym(66)!( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)
(22,27)(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);
s4 := Sym(66)!(63,64);
s5 := Sym(66)!(65,66);
poly := sub<Sym(66)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope