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Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*1200b
if this polytope has a name.
Group : SmallGroup(1200,961)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 150, 300, 20
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,4}*400
   6-fold quotients : {10,4}*200
   25-fold quotients : {6,4}*48a
   50-fold quotients : {6,2}*24
   75-fold quotients : {2,4}*16
   100-fold quotients : {3,2}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := ( 1,31)( 2,42)( 3,28)( 4,39)( 5,50)( 6,26)( 7,37)( 8,48)( 9,34)(10,45)
(11,46)(12,32)(13,43)(14,29)(15,40)(16,41)(17,27)(18,38)(19,49)(20,35)(21,36)
(22,47)(23,33)(24,44)(25,30)(51,56)(52,67)(54,64)(55,75)(57,62)(58,73)(60,70)
(61,71)(63,68)(69,74);;
s2 := ( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)(19,21)
(27,34)(28,37)(29,45)(30,48)(31,38)(32,41)(33,49)(36,50)(40,42)(44,46)(52,59)
(53,62)(54,70)(55,73)(56,63)(57,66)(58,74)(61,75)(65,67)(69,71);;
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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s1*s2*s0*s1*s0*s2*s1*s2*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)!( 1,31)( 2,42)( 3,28)( 4,39)( 5,50)( 6,26)( 7,37)( 8,48)( 9,34)
(10,45)(11,46)(12,32)(13,43)(14,29)(15,40)(16,41)(17,27)(18,38)(19,49)(20,35)
(21,36)(22,47)(23,33)(24,44)(25,30)(51,56)(52,67)(54,64)(55,75)(57,62)(58,73)
(60,70)(61,71)(63,68)(69,74);
s2 := Sym(75)!( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)
(19,21)(27,34)(28,37)(29,45)(30,48)(31,38)(32,41)(33,49)(36,50)(40,42)(44,46)
(52,59)(53,62)(54,70)(55,73)(56,63)(57,66)(58,74)(61,75)(65,67)(69,71);
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*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope