Polytope of Type {2,6,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,60}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5901)
Rank : 4
Schlafli Type : {2,6,60}
Number of vertices, edges, etc : 2, 6, 180, 60
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   3-fold quotients : {2,6,20}*480b
   5-fold quotients : {2,6,12}*288d
   15-fold quotients : {2,6,4}*96b
   30-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

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