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Polytope of Type {6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2}*576b
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {6,6,2}
Number of vertices, edges, etc : 24, 72, 24, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2} of size 1152
   {6,6,2,3} of size 1728
Vertex Figure Of :
   {2,6,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,2}*288
   3-fold quotients : {6,6,2}*192
   4-fold quotients : {6,6,2}*144c
   6-fold quotients : {3,6,2}*96, {6,3,2}*96
   8-fold quotients : {3,6,2}*72
   12-fold quotients : {3,3,2}*48, {6,2,2}*48
   24-fold quotients : {3,2,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,2}*1152a, {6,12,2}*1152c, {6,6,2}*1152b, {12,6,2}*1152d, {6,6,4}*1152f, {6,12,2}*1152e
   3-fold covers : {18,6,2}*1728, {6,6,2}*1728a, {6,6,6}*1728f, {6,6,2}*1728c
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,25)(14,27)(15,26)(16,28)(17,33)
(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(38,39)(41,45)(42,47)(43,46)
(44,48)(49,61)(50,63)(51,62)(52,64)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)
(59,66)(60,68);;
s1 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)
(11,60)(12,59)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)(21,45)
(22,46)(23,48)(24,47)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)(32,63)
(33,69)(34,70)(35,72)(36,71);;
s2 := ( 1, 4)( 5, 8)( 9,12)(13,28)(14,26)(15,27)(16,25)(17,32)(18,30)(19,31)
(20,29)(21,36)(22,34)(23,35)(24,33)(37,40)(41,44)(45,48)(49,64)(50,62)(51,63)
(52,61)(53,68)(54,66)(55,67)(56,65)(57,72)(58,70)(59,71)(60,69);;
s3 := (73,74);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,25)(14,27)(15,26)(16,28)
(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(38,39)(41,45)(42,47)
(43,46)(44,48)(49,61)(50,63)(51,62)(52,64)(53,69)(54,71)(55,70)(56,72)(57,65)
(58,67)(59,66)(60,68);
s1 := Sym(74)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)
(10,58)(11,60)(12,59)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)
(21,45)(22,46)(23,48)(24,47)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)
(32,63)(33,69)(34,70)(35,72)(36,71);
s2 := Sym(74)!( 1, 4)( 5, 8)( 9,12)(13,28)(14,26)(15,27)(16,25)(17,32)(18,30)
(19,31)(20,29)(21,36)(22,34)(23,35)(24,33)(37,40)(41,44)(45,48)(49,64)(50,62)
(51,63)(52,61)(53,68)(54,66)(55,67)(56,65)(57,72)(58,70)(59,71)(60,69);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >; 
 

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