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Polytope of Type {8,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3,2}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {8,3,2}
Number of vertices, edges, etc : 16, 24, 6, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,3,2,2} of size 384
   {8,3,2,3} of size 576
   {8,3,2,4} of size 768
   {8,3,2,5} of size 960
   {8,3,2,6} of size 1152
   {8,3,2,7} of size 1344
   {8,3,2,9} of size 1728
   {8,3,2,10} of size 1920
Vertex Figure Of :
   {2,8,3,2} of size 384
   {4,8,3,2} of size 768
   {6,8,3,2} of size 1152
   {10,8,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3,2}*96
   4-fold quotients : {4,3,2}*48
   8-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6,2}*384b
   3-fold covers : {8,9,2}*576, {24,3,2}*576, {8,3,6}*576
   4-fold covers : {8,3,2}*768, {8,12,2}*768e, {8,6,2}*768f, {8,12,2}*768h, {8,6,4}*768c, {8,3,4}*768b
   5-fold covers : {8,15,2}*960
   6-fold covers : {8,18,2}*1152b, {24,6,2}*1152b, {8,6,6}*1152b, {8,6,6}*1152c, {24,6,2}*1152e
   7-fold covers : {8,21,2}*1344
   9-fold covers : {8,27,2}*1728, {24,9,2}*1728, {24,3,2}*1728, {8,9,6}*1728, {8,3,6}*1728, {24,3,6}*1728
   10-fold covers : {8,6,10}*1920a, {40,6,2}*1920c, {8,30,2}*1920b
Permutation Representation (GAP) :
s0 := ( 1,11)( 2, 7)( 3, 6)( 4,27)( 5,29)( 8,12)( 9,16)(10,18)(13,15)(14,17)
(19,44)(20,48)(21,43)(22,46)(23,47)(24,45)(25,28)(26,30)(31,39)(32,41)(33,37)
(34,40)(35,42)(36,38);;
s1 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)
(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)
(39,40);;
s2 := ( 1, 5)( 2,14)( 3,10)( 6,18)( 7,17)( 8,26)( 9,13)(11,29)(12,30)(15,16)
(19,21)(20,42)(22,24)(23,41)(31,33)(32,47)(34,36)(35,48)(37,39)(38,40)(43,44)
(45,46);;
s3 := (49,50);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!( 1,11)( 2, 7)( 3, 6)( 4,27)( 5,29)( 8,12)( 9,16)(10,18)(13,15)
(14,17)(19,44)(20,48)(21,43)(22,46)(23,47)(24,45)(25,28)(26,30)(31,39)(32,41)
(33,37)(34,40)(35,42)(36,38);
s1 := Sym(50)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)
(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)
(36,48)(39,40);
s2 := Sym(50)!( 1, 5)( 2,14)( 3,10)( 6,18)( 7,17)( 8,26)( 9,13)(11,29)(12,30)
(15,16)(19,21)(20,42)(22,24)(23,41)(31,33)(32,47)(34,36)(35,48)(37,39)(38,40)
(43,44)(45,46);
s3 := Sym(50)!(49,50);
poly := sub<Sym(50)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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