Polytope of Type {2,2,10,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,6,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 6
Schlafli Type : {2,2,10,6,3}
Number of vertices, edges, etc : 2, 2, 10, 30, 9, 3
Order of s₀s₁s₂s₃s₄s₅ : 30
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,2,10,2,3}*480
   5-fold quotients : {2,2,2,6,3}*288
   6-fold quotients : {2,2,5,2,3}*240
   15-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48);;
s3 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)
(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)
(44,47);;
s4 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,40)(21,41)(22,42)(23,43)(24,44)
(25,35)(26,36)(27,37)(28,38)(29,39)(30,45)(31,46)(32,47)(33,48)(34,49);;
s5 := ( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,30)(11,31)(12,32)(13,33)(14,34)
(15,25)(16,26)(17,27)(18,28)(19,29)(40,45)(41,46)(42,47)(43,48)(44,49);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!(1,2);
s1 := Sym(49)!(3,4);
s2 := Sym(49)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48);
s3 := Sym(49)!( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)
(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)
(44,47);
s4 := Sym(49)!( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,40)(21,41)(22,42)(23,43)
(24,44)(25,35)(26,36)(27,37)(28,38)(29,39)(30,45)(31,46)(32,47)(33,48)(34,49);
s5 := Sym(49)!( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,30)(11,31)(12,32)(13,33)
(14,34)(15,25)(16,26)(17,27)(18,28)(19,29)(40,45)(41,46)(42,47)(43,48)(44,49);
poly := sub<Sym(49)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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