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Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*864a
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 18, 108, 54
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,12,2} of size 1728
Vertex Figure Of :
   {2,2,4,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,12}*432
   3-fold quotients : {2,4,4}*288
   6-fold quotients : {2,4,4}*144
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,12}*1728a, {2,4,12}*1728a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)
(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)
(45,54)(46,56)(47,55);;
s2 := ( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(15,16)(18,26)(19,25)
(20,24)(27,28)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(42,43)(45,53)
(46,52)(47,51)(54,55);;
s3 := ( 3,33)( 4,35)( 5,34)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,42)
(13,44)(14,43)(15,39)(16,41)(17,40)(18,45)(19,47)(20,46)(21,51)(22,53)(23,52)
(24,48)(25,50)(26,49)(27,54)(28,56)(29,55);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(56)!(1,2);
s1 := Sym(56)!( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)
(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)
(44,52)(45,54)(46,56)(47,55);
s2 := Sym(56)!( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(15,16)(18,26)
(19,25)(20,24)(27,28)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(42,43)
(45,53)(46,52)(47,51)(54,55);
s3 := Sym(56)!( 3,33)( 4,35)( 5,34)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)
(12,42)(13,44)(14,43)(15,39)(16,41)(17,40)(18,45)(19,47)(20,46)(21,51)(22,53)
(23,52)(24,48)(25,50)(26,49)(27,54)(28,56)(29,55);
poly := sub<Sym(56)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >; 
 

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