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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}*900
if this polytope has a name.
Group : SmallGroup(900,95)
Rank : 3
Schlafli Type : {6,30}
Number of vertices, edges, etc : 15, 225, 75
Order of s0s1s2 : 3
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,30,2} of size 1800
Vertex Figure Of :
   {2,6,30} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,10}*300
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,30}*1800c
Permutation Representation (GAP) :
s0 := ( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)(18,21)
(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)(52,74)
(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);;
s1 := ( 2, 5)( 3, 4)( 6, 9)( 7, 8)(11,12)(13,15)(16,20)(17,19)(21,23)(24,25)
(26,51)(27,55)(28,54)(29,53)(30,52)(31,59)(32,58)(33,57)(34,56)(35,60)(36,62)
(37,61)(38,65)(39,64)(40,63)(41,70)(42,69)(43,68)(44,67)(45,66)(46,73)(47,72)
(48,71)(49,75)(50,74);;
s2 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)(10,28)
(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)(21,37)
(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)(62,71)
(63,75)(64,74)(65,73)(66,67)(68,70);;
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*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(75)!( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)
(18,21)(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)
(52,74)(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);
s1 := Sym(75)!( 2, 5)( 3, 4)( 6, 9)( 7, 8)(11,12)(13,15)(16,20)(17,19)(21,23)
(24,25)(26,51)(27,55)(28,54)(29,53)(30,52)(31,59)(32,58)(33,57)(34,56)(35,60)
(36,62)(37,61)(38,65)(39,64)(40,63)(41,70)(42,69)(43,68)(44,67)(45,66)(46,73)
(47,72)(48,71)(49,75)(50,74);
s2 := Sym(75)!( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)
(10,28)(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)
(21,37)(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)
(62,71)(63,75)(64,74)(65,73)(66,67)(68,70);
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*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 
References : None.
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