Polytope of Type {6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240594)
Rank : 4
Schlafli Type : {6,6,4}
Number of vertices, edges, etc : 40, 120, 80, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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 : {6,6,4}*960, {6,6,2}*960
   4-fold quotients : {6,6,2}*480a, {6,6,2}*480b, {6,6,2}*480c
   8-fold quotients : {6,6,2}*240
   60-fold quotients : {2,2,4}*32
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
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