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Polytope of Type {2,4,6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6,2}*1152a
if this polytope has a name.
Group : SmallGroup(1152,153175)
Rank : 6
Schlafli Type : {2,4,6,6,2}
Number of vertices, edges, etc : 2, 4, 12, 18, 6, 2
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   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 : {2,2,6,6,2}*576a
   3-fold quotients : {2,4,2,6,2}*384, {2,4,6,2,2}*384a
   6-fold quotients : {2,4,2,3,2}*192, {2,2,2,6,2}*192, {2,2,6,2,2}*192
   9-fold quotients : {2,4,2,2,2}*128
   12-fold quotients : {2,2,2,3,2}*96, {2,2,3,2,2}*96
   18-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);;
s2 := ( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)(12,30)
(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35);;
s3 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)
(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);;
s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37);;
s5 := (39,40);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!(1,2);
s1 := Sym(40)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);
s2 := Sym(40)!( 3,21)( 4,22)( 5,23)( 6,27)( 7,28)( 8,29)( 9,24)(10,25)(11,26)
(12,30)(13,31)(14,32)(15,36)(16,37)(17,38)(18,33)(19,34)(20,35);
s3 := Sym(40)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)
(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);
s4 := Sym(40)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37);
s5 := Sym(40)!(39,40);
poly := sub<Sym(40)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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