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Polytope of Type {2,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,24}*192
if this polytope has a name.
Group : SmallGroup(192,1299)
Rank : 4
Schlafli Type : {2,2,24}
Number of vertices, edges, etc : 2, 2, 24, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,24,2} of size 384
   {2,2,24,4} of size 768
   {2,2,24,4} of size 768
   {2,2,24,4} of size 768
   {2,2,24,4} of size 768
   {2,2,24,6} of size 1152
   {2,2,24,6} of size 1152
   {2,2,24,6} of size 1152
   {2,2,24,3} of size 1152
   {2,2,24,10} of size 1920
Vertex Figure Of :
   {2,2,2,24} of size 384
   {3,2,2,24} of size 576
   {4,2,2,24} of size 768
   {5,2,2,24} of size 960
   {6,2,2,24} of size 1152
   {7,2,2,24} of size 1344
   {9,2,2,24} of size 1728
   {10,2,2,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,12}*96
   3-fold quotients : {2,2,8}*64
   4-fold quotients : {2,2,6}*48
   6-fold quotients : {2,2,4}*32
   8-fold quotients : {2,2,3}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,24}*384a, {4,2,24}*384, {2,2,48}*384
   3-fold covers : {2,2,72}*576, {2,6,24}*576a, {2,6,24}*576b, {6,2,24}*576
   4-fold covers : {2,4,24}*768a, {2,8,24}*768b, {2,8,24}*768c, {8,2,24}*768, {4,4,24}*768a, {2,4,48}*768a, {2,4,48}*768b, {4,2,48}*768, {2,2,96}*768, {2,4,24}*768c
   5-fold covers : {2,10,24}*960, {10,2,24}*960, {2,2,120}*960
   6-fold covers : {2,4,72}*1152a, {6,4,24}*1152a, {2,12,24}*1152a, {2,12,24}*1152b, {4,2,72}*1152, {4,6,24}*1152b, {4,6,24}*1152c, {12,2,24}*1152, {2,2,144}*1152, {2,6,48}*1152b, {2,6,48}*1152c, {6,2,48}*1152
   7-fold covers : {2,14,24}*1344, {14,2,24}*1344, {2,2,168}*1344
   9-fold covers : {2,2,216}*1728, {2,6,72}*1728a, {2,6,72}*1728b, {6,2,72}*1728, {2,18,24}*1728a, {18,2,24}*1728, {6,6,24}*1728a, {2,6,24}*1728a, {2,6,24}*1728b, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728d, {6,6,24}*1728e, {2,6,24}*1728f, {2,6,24}*1728h
   10-fold covers : {2,4,120}*1920a, {10,4,24}*1920a, {2,20,24}*1920a, {4,2,120}*1920, {4,10,24}*1920, {20,2,24}*1920, {2,2,240}*1920, {2,10,48}*1920, {10,2,48}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,26)(24,25)
(27,28);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,12)(10,14)(13,23)(15,18)(16,20)(19,27)(21,24)
(22,25)(26,28);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!(1,2);
s1 := Sym(28)!(3,4);
s2 := Sym(28)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,26)
(24,25)(27,28);
s3 := Sym(28)!( 5,11)( 6, 8)( 7,17)( 9,12)(10,14)(13,23)(15,18)(16,20)(19,27)
(21,24)(22,25)(26,28);
poly := sub<Sym(28)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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