Polytope of Type {15,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 4
Schlafli Type : {15,6,6}
Number of vertices, edges, etc : 20, 60, 24, 6
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {15,6,2}*480
   5-fold quotients : {3,6,6}*288
   12-fold quotients : {5,2,6}*120
   15-fold quotients : {3,6,2}*96
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {3,3,2}*48
   36-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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