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Polytope of Type {6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,30}*1800b
if this polytope has a name.
Group : SmallGroup(1800,575)
Rank : 3
Schlafli Type : {6,30}
Number of vertices, edges, etc : 30, 450, 150
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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,10}*600a
   6-fold quotients : {6,10}*300
   25-fold quotients : {6,6}*72c
   50-fold quotients : {3,6}*36
   75-fold quotients : {6,2}*24
   150-fold quotients : {3,2}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 7)( 8,10)(11,13)(14,15)(16,19)(17,18)(21,25)(22,24)
(26,51)(27,55)(28,54)(29,53)(30,52)(31,57)(32,56)(33,60)(34,59)(35,58)(36,63)
(37,62)(38,61)(39,65)(40,64)(41,69)(42,68)(43,67)(44,66)(45,70)(46,75)(47,74)
(48,73)(49,72)(50,71);;
s1 := ( 1,26)( 2,50)( 3,44)( 4,38)( 5,32)( 6,31)( 7,30)( 8,49)( 9,43)(10,37)
(11,36)(12,35)(13,29)(14,48)(15,42)(16,41)(17,40)(18,34)(19,28)(20,47)(21,46)
(22,45)(23,39)(24,33)(25,27)(52,75)(53,69)(54,63)(55,57)(58,74)(59,68)(60,62)
(64,73)(65,67)(70,72);;
s2 := ( 1,12)( 2,11)( 3,15)( 4,14)( 5,13)( 6, 7)( 8,10)(16,22)(17,21)(18,25)
(19,24)(20,23)(26,62)(27,61)(28,65)(29,64)(30,63)(31,57)(32,56)(33,60)(34,59)
(35,58)(36,52)(37,51)(38,55)(39,54)(40,53)(41,72)(42,71)(43,75)(44,74)(45,73)
(46,67)(47,66)(48,70)(49,69)(50,68);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(75)!( 2, 5)( 3, 4)( 6, 7)( 8,10)(11,13)(14,15)(16,19)(17,18)(21,25)
(22,24)(26,51)(27,55)(28,54)(29,53)(30,52)(31,57)(32,56)(33,60)(34,59)(35,58)
(36,63)(37,62)(38,61)(39,65)(40,64)(41,69)(42,68)(43,67)(44,66)(45,70)(46,75)
(47,74)(48,73)(49,72)(50,71);
s1 := Sym(75)!( 1,26)( 2,50)( 3,44)( 4,38)( 5,32)( 6,31)( 7,30)( 8,49)( 9,43)
(10,37)(11,36)(12,35)(13,29)(14,48)(15,42)(16,41)(17,40)(18,34)(19,28)(20,47)
(21,46)(22,45)(23,39)(24,33)(25,27)(52,75)(53,69)(54,63)(55,57)(58,74)(59,68)
(60,62)(64,73)(65,67)(70,72);
s2 := Sym(75)!( 1,12)( 2,11)( 3,15)( 4,14)( 5,13)( 6, 7)( 8,10)(16,22)(17,21)
(18,25)(19,24)(20,23)(26,62)(27,61)(28,65)(29,64)(30,63)(31,57)(32,56)(33,60)
(34,59)(35,58)(36,52)(37,51)(38,55)(39,54)(40,53)(41,72)(42,71)(43,75)(44,74)
(45,73)(46,67)(47,66)(48,70)(49,69)(50,68);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
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