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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2,2}*384
if this polytope has a name.
Group : SmallGroup(384,19745)
Rank : 5
Schlafli Type : {6,8,2,2}
Number of vertices, edges, etc : 6, 24, 8, 2, 2
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2,2,2} of size 768
   {6,8,2,2,3} of size 1152
   {6,8,2,2,5} of size 1920
Vertex Figure Of :
   {2,6,8,2,2} of size 768
   {3,6,8,2,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,2,2}*192a
   3-fold quotients : {2,8,2,2}*128
   4-fold quotients : {6,2,2,2}*96
   6-fold quotients : {2,4,2,2}*64
   8-fold quotients : {3,2,2,2}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8,4,2}*768a, {12,8,2,2}*768a, {6,8,2,4}*768, {6,16,2,2}*768
   3-fold covers : {18,8,2,2}*1152, {6,8,2,6}*1152, {6,8,6,2}*1152, {6,24,2,2}*1152a, {6,24,2,2}*1152b
   5-fold covers : {30,8,2,2}*1920, {6,8,2,10}*1920, {6,8,10,2}*1920, {6,40,2,2}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)(19,22)
(20,23);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)(17,20)
(21,23)(22,24);;
s3 := (25,26);;
s4 := (27,28);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);
s1 := Sym(28)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)
(19,22)(20,23);
s2 := Sym(28)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)
(17,20)(21,23)(22,24);
s3 := Sym(28)!(25,26);
s4 := Sym(28)!(27,28);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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