Polytope of Type {3,6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240594)
Rank : 5
Schlafli Type : {3,6,6,4}
Number of vertices, edges, etc : 5, 20, 40, 20, 4
Order of s₀s₁s₂s₃s₄ : 20
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, {3,6,6,2}*960
   4-fold quotients : {3,3,6,2}*480, {3,6,3,2}*480
   8-fold quotients : {3,3,3,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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