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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,6,2}*576
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 5
Schlafli Type : {6,4,6,2}
Number of vertices, edges, etc : 6, 12, 12, 6, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,6,2,2} of size 1152
   {6,4,6,2,3} of size 1728
Vertex Figure Of :
   {2,6,4,6,2} of size 1152
   {3,6,4,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,6,2}*288
   3-fold quotients : {2,4,6,2}*192a, {6,4,2,2}*192a
   4-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   6-fold quotients : {2,2,6,2}*96, {6,2,2,2}*96
   8-fold quotients : {3,2,3,2}*72
   9-fold quotients : {2,4,2,2}*64
   12-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,4,12,2}*1152, {12,4,6,2}*1152, {6,4,6,4}*1152a, {6,8,6,2}*1152
   3-fold covers : {6,4,18,2}*1728, {18,4,6,2}*1728, {6,12,6,2}*1728a, {6,12,6,2}*1728b, {6,4,6,6}*1728a, {6,4,6,6}*1728b, {6,12,6,2}*1728f, {6,12,6,2}*1728g
Permutation Representation (GAP) :
s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)
(32,35)(33,36);;
s1 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,31)(20,32)(21,33)(22,28)
(23,29)(24,30)(25,34)(26,35)(27,36);;
s2 := ( 1,19)( 2,21)( 3,20)( 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);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35);;
s4 := (37,38);;
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, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(38)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)
(31,34)(32,35)(33,36);
s1 := Sym(38)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,31)(20,32)(21,33)
(22,28)(23,29)(24,30)(25,34)(26,35)(27,36);
s2 := Sym(38)!( 1,19)( 2,21)( 3,20)( 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);
s3 := Sym(38)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35);
s4 := Sym(38)!(37,38);
poly := sub<Sym(38)|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, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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