Polytope of Type {2,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,30}*1800
if this polytope has a name.
Group : SmallGroup(1800,586)
Rank : 4
Schlafli Type : {2,6,30}
Number of vertices, edges, etc : 2, 15, 225, 75
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,6,10}*600
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)
(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)
(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);;
s2 := ( 4, 7)( 5, 6)( 8,11)( 9,10)(13,14)(15,17)(18,22)(19,21)(23,25)(26,27)
(28,53)(29,57)(30,56)(31,55)(32,54)(33,61)(34,60)(35,59)(36,58)(37,62)(38,64)
(39,63)(40,67)(41,66)(42,65)(43,72)(44,71)(45,70)(46,69)(47,68)(48,75)(49,74)
(50,73)(51,77)(52,76);;
s3 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,29)( 9,28)(10,32)(11,31)(12,30)
(13,49)(14,48)(15,52)(16,51)(17,50)(18,44)(19,43)(20,47)(21,46)(22,45)(23,39)
(24,38)(25,42)(26,41)(27,40)(53,59)(54,58)(55,62)(56,61)(57,60)(63,74)(64,73)
(65,77)(66,76)(67,75)(68,69)(70,72);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)
(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)
(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);
s2 := Sym(77)!( 4, 7)( 5, 6)( 8,11)( 9,10)(13,14)(15,17)(18,22)(19,21)(23,25)
(26,27)(28,53)(29,57)(30,56)(31,55)(32,54)(33,61)(34,60)(35,59)(36,58)(37,62)
(38,64)(39,63)(40,67)(41,66)(42,65)(43,72)(44,71)(45,70)(46,69)(47,68)(48,75)
(49,74)(50,73)(51,77)(52,76);
s3 := Sym(77)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,29)( 9,28)(10,32)(11,31)
(12,30)(13,49)(14,48)(15,52)(16,51)(17,50)(18,44)(19,43)(20,47)(21,46)(22,45)
(23,39)(24,38)(25,42)(26,41)(27,40)(53,59)(54,58)(55,62)(56,61)(57,60)(63,74)
(64,73)(65,77)(66,76)(67,75)(68,69)(70,72);
poly := sub<Sym(77)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

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