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Polytope of Type {24,2,2}

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

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