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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3,4}*864
if this polytope has a name.
Group : SmallGroup(864,4000)
Rank : 5
Schlafli Type : {2,6,3,4}
Number of vertices, edges, etc : 2, 18, 27, 18, 4
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,3,4,2} of size 1728
Vertex Figure Of :
   {2,2,6,3,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,3,4}*288
   9-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,3,4}*1728a, {2,6,3,4}*1728, {2,6,6,4}*1728e, {2,6,6,4}*1728f
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)
(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);;
s2 := ( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)(12,25)
(13,24)(14,26)(28,29)(32,33)(36,37);;
s3 := ( 5, 6)( 9,10)(13,14)(15,35)(16,36)(17,38)(18,37)(19,27)(20,28)(21,30)
(22,29)(23,31)(24,32)(25,34)(26,33);;
s4 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(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, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)
(20,36)(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);
s2 := Sym(38)!( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)
(12,25)(13,24)(14,26)(28,29)(32,33)(36,37);
s3 := Sym(38)!( 5, 6)( 9,10)(13,14)(15,35)(16,36)(17,38)(18,37)(19,27)(20,28)
(21,30)(22,29)(23,31)(24,32)(25,34)(26,33);
s4 := Sym(38)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(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, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >; 
 

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