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

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope