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Polytope of Type {6,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,8}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 4
Schlafli Type : {6,2,8}
Number of vertices, edges, etc : 6, 6, 8, 8
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,8,2} of size 384
   {6,2,8,4} of size 768
   {6,2,8,4} of size 768
   {6,2,8,6} of size 1152
   {6,2,8,3} of size 1152
   {6,2,8,10} of size 1920
Vertex Figure Of :
   {2,6,2,8} of size 384
   {3,6,2,8} of size 576
   {4,6,2,8} of size 768
   {3,6,2,8} of size 768
   {4,6,2,8} of size 768
   {4,6,2,8} of size 768
   {4,6,2,8} of size 1152
   {6,6,2,8} of size 1152
   {6,6,2,8} of size 1152
   {6,6,2,8} of size 1152
   {9,6,2,8} of size 1728
   {3,6,2,8} of size 1728
   {6,6,2,8} of size 1728
   {10,6,2,8} of size 1920
   {4,6,2,8} of size 1920
   {5,6,2,8} of size 1920
   {6,6,2,8} of size 1920
   {5,6,2,8} of size 1920
   {5,6,2,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,8}*96, {6,2,4}*96
   3-fold quotients : {2,2,8}*64
   4-fold quotients : {3,2,4}*48, {6,2,2}*48
   6-fold quotients : {2,2,4}*32
   8-fold quotients : {3,2,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,8}*384, {6,4,8}*384a, {6,2,16}*384
   3-fold covers : {18,2,8}*576, {6,2,24}*576, {6,6,8}*576a, {6,6,8}*576c
   4-fold covers : {6,4,8}*768a, {6,8,8}*768a, {6,8,8}*768b, {24,2,8}*768, {12,4,8}*768a, {6,4,16}*768a, {6,4,16}*768b, {12,2,16}*768, {6,2,32}*768, {6,4,8}*768c
   5-fold covers : {6,2,40}*960, {6,10,8}*960, {30,2,8}*960
   6-fold covers : {18,4,8}*1152a, {6,12,8}*1152b, {6,12,8}*1152c, {6,4,24}*1152a, {36,2,8}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {12,2,24}*1152, {18,2,16}*1152, {6,6,16}*1152b, {6,6,16}*1152c, {6,2,48}*1152
   7-fold covers : {6,2,56}*1344, {6,14,8}*1344, {42,2,8}*1344
   9-fold covers : {54,2,8}*1728, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {6,18,8}*1728a, {18,6,8}*1728a, {6,6,8}*1728b, {18,6,8}*1728b, {6,6,8}*1728c, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e, {6,6,8}*1728e, {6,6,24}*1728f, {6,6,8}*1728f, {6,6,8}*1728g
   10-fold covers : {30,4,8}*1920a, {6,20,8}*1920a, {6,4,40}*1920a, {60,2,8}*1920, {12,10,8}*1920, {12,2,40}*1920, {30,2,16}*1920, {6,10,16}*1920, {6,2,80}*1920
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,13);;
s3 := ( 7, 8)( 9,10)(11,12)(13,14);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(3,4)(5,6);
s1 := Sym(14)!(1,5)(2,3)(4,6);
s2 := Sym(14)!( 8, 9)(10,11)(12,13);
s3 := Sym(14)!( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(14)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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