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Polytope of Type {30,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,3}*900
if this polytope has a name.
Group : SmallGroup(900,95)
Rank : 3
Schlafli Type : {30,3}
Number of vertices, edges, etc : 150, 225, 15
Order of s0s1s2 : 6
Order of s0s1s2s1 : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,3,2} of size 1800
Vertex Figure Of :
   {2,30,3} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,3}*300
   25-fold quotients : {6,3}*36
   75-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,6}*1800c
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)(34,73)
(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)(45,62)
(46,56)(47,60)(48,59)(49,58)(50,57);;
s1 := ( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,35)( 7,34)( 8,33)( 9,32)(10,31)
(11,38)(12,37)(13,36)(14,40)(15,39)(16,41)(17,45)(18,44)(19,43)(20,42)(21,49)
(22,48)(23,47)(24,46)(25,50)(51,52)(53,55)(56,60)(57,59)(61,63)(64,65)(67,70)
(68,69)(71,74)(72,73);;
s2 := ( 2, 8)( 3,15)( 4,17)( 5,24)( 6,18)( 7,25)(10,11)(13,19)(14,21)(16,22)
(26,51)(27,58)(28,65)(29,67)(30,74)(31,68)(32,75)(33,52)(34,59)(35,61)(36,60)
(37,62)(38,69)(39,71)(40,53)(41,72)(42,54)(43,56)(44,63)(45,70)(46,64)(47,66)
(48,73)(49,55)(50,57);;
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, s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)
(13,19)(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)
(34,73)(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)
(45,62)(46,56)(47,60)(48,59)(49,58)(50,57);
s1 := Sym(75)!( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,35)( 7,34)( 8,33)( 9,32)
(10,31)(11,38)(12,37)(13,36)(14,40)(15,39)(16,41)(17,45)(18,44)(19,43)(20,42)
(21,49)(22,48)(23,47)(24,46)(25,50)(51,52)(53,55)(56,60)(57,59)(61,63)(64,65)
(67,70)(68,69)(71,74)(72,73);
s2 := Sym(75)!( 2, 8)( 3,15)( 4,17)( 5,24)( 6,18)( 7,25)(10,11)(13,19)(14,21)
(16,22)(26,51)(27,58)(28,65)(29,67)(30,74)(31,68)(32,75)(33,52)(34,59)(35,61)
(36,60)(37,62)(38,69)(39,71)(40,53)(41,72)(42,54)(43,56)(44,63)(45,70)(46,64)
(47,66)(48,73)(49,55)(50,57);
poly := sub<Sym(75)|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, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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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