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Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1440g
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 120, 360, 24
Order of s0s1s2 : 60
Order of s0s1s2s1 : 6
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) :
   3-fold quotients : {30,6}*480
   4-fold quotients : {30,6}*360a
   5-fold quotients : {6,6}*288a
   6-fold quotients : {15,6}*240
   10-fold quotients : {6,3}*144
   12-fold quotients : {10,6}*120
   15-fold quotients : {6,6}*96
   20-fold quotients : {6,6}*72b
   30-fold quotients : {3,6}*48, {6,3}*48
   36-fold quotients : {10,2}*40
   40-fold quotients : {6,3}*36
   60-fold quotients : {3,3}*24, {2,6}*24
   72-fold quotients : {5,2}*20
   120-fold quotients : {2,3}*12
   180-fold quotients : {2,2}*8
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)(21,45)
(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,57)(30,60)(31,59)(32,58)
(33,53)(34,56)(35,55)(36,54)(37,49)(38,52)(39,51)(40,50);;
s2 := ( 1,22)( 2,21)( 3,23)( 4,24)( 5,26)( 6,25)( 7,27)( 8,28)( 9,30)(10,29)
(11,31)(12,32)(13,34)(14,33)(15,35)(16,36)(17,38)(18,37)(19,39)(20,40)(41,42)
(45,46)(49,50)(53,54)(57,58);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*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)
(21,45)(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,57)(30,60)(31,59)
(32,58)(33,53)(34,56)(35,55)(36,54)(37,49)(38,52)(39,51)(40,50);
s2 := Sym(60)!( 1,22)( 2,21)( 3,23)( 4,24)( 5,26)( 6,25)( 7,27)( 8,28)( 9,30)
(10,29)(11,31)(12,32)(13,34)(14,33)(15,35)(16,36)(17,38)(18,37)(19,39)(20,40)
(41,42)(45,46)(49,50)(53,54)(57,58);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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