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Polytope of Type {6,2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,8,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,152548)
Rank : 5
Schlafli Type : {6,2,8,6}
Number of vertices, edges, etc : 6, 6, 8, 24, 6
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,8,6}*576, {6,2,4,6}*576a
   3-fold quotients : {2,2,8,6}*384, {6,2,8,2}*384
   4-fold quotients : {3,2,4,6}*288a, {6,2,2,6}*288
   6-fold quotients : {3,2,8,2}*192, {2,2,4,6}*192a, {6,2,4,2}*192
   8-fold quotients : {3,2,2,6}*144, {6,2,2,3}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {3,2,4,2}*96, {2,2,2,6}*96, {6,2,2,2}*96
   16-fold quotients : {3,2,2,3}*72
   18-fold quotients : {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*48, {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22)(20,23)(24,27)(25,28);;
s3 := ( 7, 8)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,25)(22,24)(23,26)
(27,30)(28,29);;
s4 := ( 7, 9)( 8,12)(11,15)(14,18)(17,21)(20,24)(23,27)(26,29);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(30)!(3,4)(5,6);
s1 := Sym(30)!(1,5)(2,3)(4,6);
s2 := Sym(30)!( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22)(20,23)(24,27)(25,28);
s3 := Sym(30)!( 7, 8)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,25)(22,24)
(23,26)(27,30)(28,29);
s4 := Sym(30)!( 7, 9)( 8,12)(11,15)(14,18)(17,21)(20,24)(23,27)(26,29);
poly := sub<Sym(30)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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