Polytope of Type {24,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,2,3}*288
if this polytope has a name.
Group : SmallGroup(288,441)
Rank : 4
Schlafli Type : {24,2,3}
Number of vertices, edges, etc : 24, 24, 3, 3
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {24,2,3,2} of size 576
   {24,2,3,3} of size 1152
   {24,2,3,4} of size 1152
   {24,2,3,6} of size 1728
Vertex Figure Of :
   {2,24,2,3} of size 576
   {4,24,2,3} of size 1152
   {4,24,2,3} of size 1152
   {4,24,2,3} of size 1152
   {4,24,2,3} of size 1152
   {6,24,2,3} of size 1728
   {6,24,2,3} of size 1728
   {6,24,2,3} of size 1728
   {3,24,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,3}*144
   3-fold quotients : {8,2,3}*96
   4-fold quotients : {6,2,3}*72
   6-fold quotients : {4,2,3}*48
   8-fold quotients : {3,2,3}*36
   12-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,2,3}*576, {24,2,6}*576
   3-fold covers : {72,2,3}*864, {24,2,9}*864, {24,6,3}*864a, {24,6,3}*864b
   4-fold covers : {96,2,3}*1152, {24,4,6}*1152a, {24,2,12}*1152, {48,2,6}*1152, {24,4,3}*1152
   5-fold covers : {24,2,15}*1440, {120,2,3}*1440
   6-fold covers : {144,2,3}*1728, {48,2,9}*1728, {48,6,3}*1728a, {72,2,6}*1728, {24,2,18}*1728, {24,6,6}*1728a, {48,6,3}*1728b, {24,6,6}*1728b, {24,6,6}*1728d, {24,6,6}*1728e
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 := (26,27);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*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(27)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(27)!( 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(27)!(26,27);
s3 := Sym(27)!(25,26);
poly := sub<Sym(27)|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*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 >;

to this polytope