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Polytope of Type {12,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,15}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {12,15}
Number of vertices, edges, etc : 48, 360, 60
Order of s0s1s2 : 20
Order of s0s1s2s1 : 60
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,15}*720c
   3-fold quotients : {12,5}*480
   4-fold quotients : {3,15}*360
   6-fold quotients : {6,5}*240b
   12-fold quotients : {3,5}*120, {6,5}*120b, {6,5}*120c
   24-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)
(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);;
s1 := ( 1, 5)( 2,22)( 3,21)( 4,23)( 6,13)( 7,19)( 8,45)( 9,43)(10,46)(11,27)
(12,24)(14,25)(15,48)(16,40)(17,36)(18,44)(20,35)(26,37)(28,34)(29,31)(30,39)
(32,47)(33,38)(41,42)(49,50);;
s2 := ( 1,12)( 2,29)( 3,21)( 4,31)( 5,13)( 6,46)( 7,36)( 8,45)( 9,27)(10,42)
(11,38)(14,44)(15,28)(16,48)(17,40)(18,23)(19,34)(20,35)(22,25)(24,41)(26,43)
(30,39)(32,37)(33,47)(50,51);;
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, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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(51)!( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)
(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);
s1 := Sym(51)!( 1, 5)( 2,22)( 3,21)( 4,23)( 6,13)( 7,19)( 8,45)( 9,43)(10,46)
(11,27)(12,24)(14,25)(15,48)(16,40)(17,36)(18,44)(20,35)(26,37)(28,34)(29,31)
(30,39)(32,47)(33,38)(41,42)(49,50);
s2 := Sym(51)!( 1,12)( 2,29)( 3,21)( 4,31)( 5,13)( 6,46)( 7,36)( 8,45)( 9,27)
(10,42)(11,38)(14,44)(15,28)(16,48)(17,40)(18,23)(19,34)(20,35)(22,25)(24,41)
(26,43)(30,39)(32,37)(33,47)(50,51);
poly := sub<Sym(51)|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, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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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