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Polytope of Type {15,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,12}*720
if this polytope has a name.
Group : SmallGroup(720,793)
Rank : 3
Schlafli Type : {15,12}
Number of vertices, edges, etc : 30, 180, 24
Order of s0s1s2 : 30
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {15,12,2} of size 1440
Vertex Figure Of :
   {2,15,12} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {15,4}*240
   4-fold quotients : {15,6}*180
   5-fold quotients : {3,12}*144
   6-fold quotients : {15,4}*120
   12-fold quotients : {15,2}*60
   15-fold quotients : {3,4}*48
   20-fold quotients : {3,6}*36
   30-fold quotients : {3,4}*24
   36-fold quotients : {5,2}*20
   60-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,24}*1440, {30,12}*1440b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)(21,41)
(22,43)(23,42)(24,44)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)
(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48);;
s1 := ( 1,25)( 2,28)( 3,27)( 4,26)( 5,21)( 6,24)( 7,23)( 8,22)( 9,37)(10,40)
(11,39)(12,38)(13,33)(14,36)(15,35)(16,34)(17,29)(18,32)(19,31)(20,30)(41,45)
(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);;
s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,44)(22,43)(23,42)(24,41)(25,48)(26,47)(27,46)(28,45)(29,52)(30,51)(31,50)
(32,49)(33,56)(34,55)(35,54)(36,53)(37,60)(38,59)(39,58)(40,57);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(60)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)
(21,41)(22,43)(23,42)(24,44)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)
(32,56)(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48);
s1 := Sym(60)!( 1,25)( 2,28)( 3,27)( 4,26)( 5,21)( 6,24)( 7,23)( 8,22)( 9,37)
(10,40)(11,39)(12,38)(13,33)(14,36)(15,35)(16,34)(17,29)(18,32)(19,31)(20,30)
(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);
s2 := Sym(60)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,44)(22,43)(23,42)(24,41)(25,48)(26,47)(27,46)(28,45)(29,52)(30,51)
(31,50)(32,49)(33,56)(34,55)(35,54)(36,53)(37,60)(38,59)(39,58)(40,57);
poly := sub<Sym(60)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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