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Polytope of Type {2,24,2}

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