Polytope of Type {6,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,3}*1800
Also Known As : {{6,6|2},{6,3}₁₀}. if this polytope has another name.
Group : SmallGroup(1800,575)
Rank : 4
Schlafli Type : {6,6,3}
Number of vertices, edges, etc : 6, 150, 75, 25
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,3}*600
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)
(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)
(47,72)(48,73)(49,74)(50,75);;
s1 := ( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,32)( 7,31)( 8,35)( 9,34)(10,33)
(11,38)(12,37)(13,36)(14,40)(15,39)(16,44)(17,43)(18,42)(19,41)(20,45)(21,50)
(22,49)(23,48)(24,47)(25,46)(52,55)(53,54)(56,57)(58,60)(61,63)(64,65)(66,69)
(67,68)(71,75)(72,74);;
s2 := ( 2,25)( 3,19)( 4,13)( 5, 7)( 8,24)( 9,18)(10,12)(14,23)(15,17)(20,22)
(27,50)(28,44)(29,38)(30,32)(33,49)(34,43)(35,37)(39,48)(40,42)(45,47)(52,75)
(53,69)(54,63)(55,57)(58,74)(59,68)(60,62)(64,73)(65,67)(70,72);;
s3 := ( 1,12)( 2,13)( 3,14)( 4,15)( 5,11)(16,24)(17,25)(18,21)(19,22)(20,23)
(26,37)(27,38)(28,39)(29,40)(30,36)(41,49)(42,50)(43,46)(44,47)(45,48)(51,62)
(52,63)(53,64)(54,65)(55,61)(66,74)(67,75)(68,71)(69,72)(70,73);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(75)!(26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)
(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)
(46,71)(47,72)(48,73)(49,74)(50,75);
s1 := Sym(75)!( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,32)( 7,31)( 8,35)( 9,34)
(10,33)(11,38)(12,37)(13,36)(14,40)(15,39)(16,44)(17,43)(18,42)(19,41)(20,45)
(21,50)(22,49)(23,48)(24,47)(25,46)(52,55)(53,54)(56,57)(58,60)(61,63)(64,65)
(66,69)(67,68)(71,75)(72,74);
s2 := Sym(75)!( 2,25)( 3,19)( 4,13)( 5, 7)( 8,24)( 9,18)(10,12)(14,23)(15,17)
(20,22)(27,50)(28,44)(29,38)(30,32)(33,49)(34,43)(35,37)(39,48)(40,42)(45,47)
(52,75)(53,69)(54,63)(55,57)(58,74)(59,68)(60,62)(64,73)(65,67)(70,72);
s3 := Sym(75)!( 1,12)( 2,13)( 3,14)( 4,15)( 5,11)(16,24)(17,25)(18,21)(19,22)
(20,23)(26,37)(27,38)(28,39)(29,40)(30,36)(41,49)(42,50)(43,46)(44,47)(45,48)
(51,62)(52,63)(53,64)(54,65)(55,61)(66,74)(67,75)(68,71)(69,72)(70,73);
poly := sub<Sym(75)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;

References : None.
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