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

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

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

Permutation Representation (Magma) :

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

to this polytope