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Polytope of Type {4,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,8}*768
if this polytope has a name.
Group : SmallGroup(768,1044755)
Rank : 5
Schlafli Type : {4,2,6,8}
Number of vertices, edges, etc : 4, 4, 6, 24, 8
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 : {4,2,6,4}*384a, {2,2,6,8}*384
   3-fold quotients : {4,2,2,8}*256
   4-fold quotients : {2,2,6,4}*192a, {4,2,6,2}*192
   6-fold quotients : {4,2,2,4}*128, {2,2,2,8}*128
   8-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   12-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   16-fold quotients : {2,2,3,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,28);;
s3 := ( 5, 7)( 6,13)( 9,10)(11,14)(12,19)(15,16)(17,20)(18,25)(21,22)(23,26)
(24,27);;
s4 := ( 5, 6)( 7,10)( 8,11)( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)
(25,27)(26,28);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!(2,3);
s1 := Sym(28)!(1,2)(3,4);
s2 := Sym(28)!( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,28);
s3 := Sym(28)!( 5, 7)( 6,13)( 9,10)(11,14)(12,19)(15,16)(17,20)(18,25)(21,22)
(23,26)(24,27);
s4 := Sym(28)!( 5, 6)( 7,10)( 8,11)( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)
(21,24)(25,27)(26,28);
poly := sub<Sym(28)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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