Polytope of Type {3,2,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,20}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5284)
Rank : 5
Schlafli Type : {3,2,6,20}
Number of vertices, edges, etc : 3, 3, 6, 60, 20
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,2,6,10}*720
   3-fold quotients : {3,2,2,20}*480
   5-fold quotients : {3,2,6,4}*288a
   6-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,2,5}*120
   15-fold quotients : {3,2,2,4}*96
   20-fold quotients : {3,2,3,2}*72
   30-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope