Polytope of Type {8,6,3,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,3,3}*1920
Also Known As : {{8,6|2},{6,3}₄,{3,3}}. if this polytope has another name.
Group : SmallGroup(1920,240560)
Rank : 5
Schlafli Type : {8,6,3,3}
Number of vertices, edges, etc : 8, 40, 20, 10, 5
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {4,6,3,3}*960
   4-fold quotients : {2,6,3,3}*480
   8-fold quotients : {2,3,3,3}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(37)!( 6,18)( 7,19)( 8,21)( 9,20)(10,14)(11,15)(12,17)(13,16)(22,34)
(23,35)(24,37)(25,36)(26,30)(27,31)(28,33)(29,32);
s1 := Sym(37)!( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,26)(11,27)(12,29)(13,28)
(14,32)(15,33)(16,30)(17,31)(18,36)(19,37)(20,34)(21,35);
s2 := Sym(37)!( 3, 4)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)
(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s3 := Sym(37)!( 2, 3)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)
(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s4 := Sym(37)!( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)
(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
poly := sub<Sym(37)|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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope