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Polytope of Type {4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2}*192a
if this polytope has a name.
Group : SmallGroup(192,1046)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 4, 24, 12, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,2,2} of size 384
   {4,12,2,3} of size 576
   {4,12,2,4} of size 768
   {4,12,2,5} of size 960
   {4,12,2,6} of size 1152
   {4,12,2,7} of size 1344
   {4,12,2,9} of size 1728
   {4,12,2,10} of size 1920
Vertex Figure Of :
   {2,4,12,2} of size 384
   {4,4,12,2} of size 768
   {6,4,12,2} of size 1152
   {3,4,12,2} of size 1152
   {6,4,12,2} of size 1728
   {10,4,12,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,2}*96, {4,6,2}*96a
   3-fold quotients : {4,4,2}*64
   4-fold quotients : {2,6,2}*48
   6-fold quotients : {2,4,2}*32, {4,2,2}*32
   8-fold quotients : {2,3,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4}*384a, {4,24,2}*384a, {4,12,2}*384a, {4,24,2}*384b, {8,12,2}*384a, {8,12,2}*384b
   3-fold covers : {4,36,2}*576a, {4,12,6}*576a, {4,12,6}*576b, {12,12,2}*576a, {12,12,2}*576b
   4-fold covers : {8,12,2}*768a, {4,24,2}*768a, {8,24,2}*768a, {8,24,2}*768b, {8,24,2}*768c, {8,24,2}*768d, {4,12,8}*768a, {8,12,4}*768a, {4,12,8}*768b, {8,12,4}*768b, {4,24,4}*768a, {4,12,4}*768a, {4,12,4}*768b, {4,24,4}*768b, {4,24,4}*768c, {4,24,4}*768d, {16,12,2}*768a, {4,48,2}*768a, {16,12,2}*768b, {4,48,2}*768b, {4,12,2}*768a, {4,24,2}*768b, {8,12,2}*768b, {4,12,4}*768e, {4,12,2}*768d
   5-fold covers : {4,12,10}*960a, {20,12,2}*960, {4,60,2}*960a
   6-fold covers : {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {8,36,2}*1152a, {4,72,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {4,24,6}*1152b, {4,24,6}*1152c, {12,24,2}*1152a, {12,24,2}*1152b, {24,12,2}*1152a, {24,12,2}*1152c, {8,36,2}*1152b, {4,72,2}*1152b, {8,12,6}*1152d, {8,12,6}*1152e, {4,24,6}*1152e, {4,24,6}*1152f, {12,24,2}*1152d, {12,24,2}*1152e, {24,12,2}*1152d, {24,12,2}*1152f, {4,36,2}*1152a, {4,12,6}*1152a, {4,12,6}*1152b, {12,12,2}*1152a, {12,12,2}*1152b
   7-fold covers : {4,12,14}*1344a, {28,12,2}*1344, {4,84,2}*1344a
   9-fold covers : {4,108,2}*1728a, {4,12,18}*1728a, {4,36,6}*1728a, {4,36,6}*1728b, {4,12,6}*1728a, {4,12,6}*1728b, {12,36,2}*1728a, {12,36,2}*1728b, {36,12,2}*1728a, {12,12,2}*1728b, {12,12,2}*1728c, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728d, {12,12,6}*1728e, {12,12,2}*1728h, {4,12,6}*1728j, {4,12,2}*1728c, {4,12,2}*1728d, {4,12,6}*1728q, {12,12,2}*1728l
   10-fold covers : {4,60,4}*1920a, {4,12,20}*1920a, {20,12,4}*1920a, {8,60,2}*1920a, {4,120,2}*1920a, {8,12,10}*1920a, {4,24,10}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {8,60,2}*1920b, {4,120,2}*1920b, {8,12,10}*1920b, {4,24,10}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {4,60,2}*1920a, {4,12,10}*1920a, {20,12,2}*1920a
Permutation Representation (GAP) :
s0 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s1 := ( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)(16,23)
(19,22)(20,21);;
s2 := ( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)(16,20);;
s3 := (25,26);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(26)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s1 := Sym(26)!( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)
(16,23)(19,22)(20,21);
s2 := Sym(26)!( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)
(16,20);
s3 := Sym(26)!(25,26);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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