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Polytope of Type {2,3,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {2,3,12}
Number of vertices, edges, etc : 2, 4, 24, 16
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,12,2} of size 384
   {2,3,12,4} of size 768
   {2,3,12,3} of size 960
   {2,3,12,6} of size 1152
   {2,3,12,10} of size 1920
   {2,3,12,6} of size 1920
Vertex Figure Of :
   {2,2,3,12} of size 384
   {3,2,3,12} of size 576
   {4,2,3,12} of size 768
   {5,2,3,12} of size 960
   {6,2,3,12} of size 1152
   {7,2,3,12} of size 1344
   {9,2,3,12} of size 1728
   {10,2,3,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,6}*96
   4-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12}*384b
   3-fold covers : {2,3,12}*576
   4-fold covers : {2,3,12}*768, {4,3,12}*768a, {2,12,12}*768b, {2,6,12}*768, {2,12,12}*768d, {4,6,12}*768b
   5-fold covers : {2,15,12}*960
   6-fold covers : {2,6,12}*1152c, {6,6,12}*1152c, {2,6,12}*1152d
   7-fold covers : {2,21,12}*1344
   9-fold covers : {2,9,12}*1728, {2,3,12}*1728, {6,3,12}*1728
   10-fold covers : {2,30,12}*1920a, {10,6,12}*1920b, {2,6,60}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)
(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)
(41,42);;
s2 := ( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)(17,42)
(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)(36,37)
(39,40);;
s3 := ( 3,46)( 4,41)( 5,42)( 6,35)( 7,49)( 8,14)( 9,13)(10,48)(11,23)(12,43)
(15,26)(16,44)(17,32)(18,31)(19,30)(20,29)(21,36)(22,45)(24,33)(25,47)(27,38)
(28,50)(34,40)(37,39);;
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*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)
(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)
(38,50)(41,42);
s2 := Sym(50)!( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)
(17,42)(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)
(36,37)(39,40);
s3 := Sym(50)!( 3,46)( 4,41)( 5,42)( 6,35)( 7,49)( 8,14)( 9,13)(10,48)(11,23)
(12,43)(15,26)(16,44)(17,32)(18,31)(19,30)(20,29)(21,36)(22,45)(24,33)(25,47)
(27,38)(28,50)(34,40)(37,39);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 >; 
 

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