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Polytope of Type {3,2,6,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,4,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,47341)
Rank : 6
Schlafli Type : {3,2,6,4,6}
Number of vertices, edges, etc : 3, 3, 6, 12, 12, 6
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 : {3,2,6,2,6}*864
   3-fold quotients : {3,2,2,4,6}*576a, {3,2,6,4,2}*576a
   4-fold quotients : {3,2,3,2,6}*432, {3,2,6,2,3}*432
   6-fold quotients : {3,2,2,2,6}*288, {3,2,6,2,2}*288
   8-fold quotients : {3,2,3,2,3}*216
   9-fold quotients : {3,2,2,4,2}*192
   12-fold quotients : {3,2,2,2,3}*144, {3,2,3,2,2}*144
   18-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)
(35,38)(36,39);;
s3 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,34)(23,35)(24,36)(25,31)
(26,32)(27,33)(28,37)(29,38)(30,39);;
s4 := ( 4,22)( 5,24)( 6,23)( 7,25)( 8,27)( 9,26)(10,28)(11,30)(12,29)(13,31)
(14,33)(15,32)(16,34)(17,36)(18,35)(19,37)(20,39)(21,38);;
s5 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38);;
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*s2*s0*s2, s1*s2*s1*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, s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(39)!(2,3);
s1 := Sym(39)!(1,2);
s2 := Sym(39)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)
(34,37)(35,38)(36,39);
s3 := Sym(39)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,34)(23,35)(24,36)
(25,31)(26,32)(27,33)(28,37)(29,38)(30,39);
s4 := Sym(39)!( 4,22)( 5,24)( 6,23)( 7,25)( 8,27)( 9,26)(10,28)(11,30)(12,29)
(13,31)(14,33)(15,32)(16,34)(17,36)(18,35)(19,37)(20,39)(21,38);
s5 := Sym(39)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38);
poly := sub<Sym(39)|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*s2*s0*s2, s1*s2*s1*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, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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