Polytope of Type {15,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6,2,2}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 5
Schlafli Type : {15,6,2,2}
Number of vertices, edges, etc : 15, 45, 6, 2, 2
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,6,2,2,2} of size 1440
Vertex Figure Of :
   {2,15,6,2,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {15,2,2,2}*240
   5-fold quotients : {3,6,2,2}*144
   9-fold quotients : {5,2,2,2}*80
   15-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,6,2,4}*1440, {15,6,4,2}*1440, {30,6,2,2}*1440c
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope