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Polytope of Type {2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 4
Schlafli Type : {2,6,8}
Number of vertices, edges, etc : 2, 6, 24, 8
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,8,2} of size 384
   {2,6,8,4} of size 768
   {2,6,8,4} of size 768
   {2,6,8,6} of size 1152
   {2,6,8,3} of size 1152
   {2,6,8,10} of size 1920
Vertex Figure Of :
   {2,2,6,8} of size 384
   {3,2,6,8} of size 576
   {4,2,6,8} of size 768
   {5,2,6,8} of size 960
   {6,2,6,8} of size 1152
   {7,2,6,8} of size 1344
   {9,2,6,8} of size 1728
   {10,2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,4}*96a
   3-fold quotients : {2,2,8}*64
   4-fold quotients : {2,6,2}*48
   6-fold quotients : {2,2,4}*32
   8-fold quotients : {2,3,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,8}*384a, {4,6,8}*384a, {2,6,16}*384
   3-fold covers : {2,18,8}*576, {2,6,24}*576a, {6,6,8}*576a, {6,6,8}*576b, {2,6,24}*576c
   4-fold covers : {2,12,8}*768a, {2,24,8}*768a, {2,24,8}*768c, {8,6,8}*768, {4,12,8}*768a, {2,12,16}*768a, {2,12,16}*768b, {4,6,16}*768a, {2,6,32}*768, {4,6,8}*768a, {2,6,8}*768g
   5-fold covers : {2,6,40}*960, {10,6,8}*960, {2,30,8}*960
   6-fold covers : {2,36,8}*1152a, {6,12,8}*1152a, {6,12,8}*1152b, {2,12,24}*1152a, {2,12,24}*1152c, {4,18,8}*1152a, {12,6,8}*1152a, {12,6,8}*1152b, {4,6,24}*1152a, {4,6,24}*1152b, {2,18,16}*1152, {6,6,16}*1152a, {6,6,16}*1152b, {2,6,48}*1152a, {2,6,48}*1152b
   7-fold covers : {2,6,56}*1344, {14,6,8}*1344, {2,42,8}*1344
   9-fold covers : {2,54,8}*1728, {2,6,72}*1728a, {2,18,24}*1728a, {2,6,24}*1728b, {6,18,8}*1728a, {6,18,8}*1728b, {18,6,8}*1728a, {6,6,8}*1728a, {6,6,8}*1728b, {2,18,24}*1728b, {2,6,24}*1728c, {6,6,24}*1728b, {6,6,24}*1728d, {2,6,24}*1728f, {6,6,8}*1728e, {6,6,24}*1728f, {6,6,24}*1728g, {2,6,8}*1728b
   10-fold covers : {2,60,8}*1920a, {10,12,8}*1920a, {2,12,40}*1920a, {4,30,8}*1920a, {20,6,8}*1920, {4,6,40}*1920a, {2,30,16}*1920, {10,6,16}*1920, {2,6,80}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(25,26);;
s2 := ( 3, 5)( 4,11)( 7, 8)( 9,12)(10,17)(13,14)(15,18)(16,23)(19,20)(21,24)
(22,25);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,22)
(23,25)(24,26);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(25,26);
s2 := Sym(26)!( 3, 5)( 4,11)( 7, 8)( 9,12)(10,17)(13,14)(15,18)(16,23)(19,20)
(21,24)(22,25);
s3 := Sym(26)!( 3, 4)( 5, 8)( 6, 9)( 7,10)(11,14)(12,15)(13,16)(17,20)(18,21)
(19,22)(23,25)(24,26);
poly := sub<Sym(26)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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