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Polytope of Type {12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2}*192c
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 4
Schlafli Type : {12,4,2}
Number of vertices, edges, etc : 12, 24, 4, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,4,2,2} of size 384
   {12,4,2,3} of size 576
   {12,4,2,4} of size 768
   {12,4,2,5} of size 960
   {12,4,2,6} of size 1152
   {12,4,2,7} of size 1344
   {12,4,2,9} of size 1728
   {12,4,2,10} of size 1920
Vertex Figure Of :
   {2,12,4,2} of size 384
   {4,12,4,2} of size 768
   {4,12,4,2} of size 768
   {4,12,4,2} of size 768
   {6,12,4,2} of size 1152
   {6,12,4,2} of size 1152
   {10,12,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,2}*96c
   4-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2}*384b
   3-fold covers : {36,4,2}*576c
   4-fold covers : {12,4,2}*768c, {12,4,4}*768d, {12,4,2}*768d, {12,4,4}*768e, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d
   5-fold covers : {60,4,2}*960c
   6-fold covers : {36,4,2}*1152b, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e
   7-fold covers : {84,4,2}*1344c
   9-fold covers : {108,4,2}*1728c, {12,12,2}*1728n
   10-fold covers : {12,4,10}*1920b, {12,20,2}*1920b, {60,4,2}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s1 := ( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)(14,42)
(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)(31,36)
(32,41)(35,45)(40,46);;
s2 := ( 1,47)( 2,45)( 3,42)( 4,48)( 5,39)( 6,37)( 7,33)( 8,44)( 9,31)(10,24)
(11,43)(12,26)(13,29)(14,38)(15,46)(16,21)(17,35)(18,20)(19,34)(22,30)(23,40)
(25,27)(28,41)(32,36);;
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*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s1 := Sym(50)!( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)
(14,42)(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)
(31,36)(32,41)(35,45)(40,46);
s2 := Sym(50)!( 1,47)( 2,45)( 3,42)( 4,48)( 5,39)( 6,37)( 7,33)( 8,44)( 9,31)
(10,24)(11,43)(12,26)(13,29)(14,38)(15,46)(16,21)(17,35)(18,20)(19,34)(22,30)
(23,40)(25,27)(28,41)(32,36);
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*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 >; 
 

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