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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,3,6}*1920
Also Known As : {{4,6|2},{6,3}4,{3,6}4}. if this polytope has another name.
Group : SmallGroup(1920,240594)
Rank : 5
Schlafli Type : {4,6,3,6}
Number of vertices, edges, etc : 4, 20, 20, 20, 10
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 : {4,6,3,3}*960, {2,6,3,6}*960
   4-fold quotients : {2,3,3,6}*480, {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 := ( 6,16)( 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);;
s1 := ( 4, 5)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,31)
(15,30)(16,33)(17,32)(18,35)(19,34)(20,37)(21,36);;
s2 := ( 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);;
s3 := ( 2, 3)( 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);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(37)!( 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);
s1 := Sym(37)!( 4, 5)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)
(14,31)(15,30)(16,33)(17,32)(18,35)(19,34)(20,37)(21,36);
s2 := 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);
s3 := Sym(37)!( 2, 3)( 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);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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