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

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

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