Polytope of Type {3,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,24}*288
if this polytope has a name.
Group : SmallGroup(288,441)
Rank : 4
Schlafli Type : {3,2,24}
Number of vertices, edges, etc : 3, 3, 24, 24
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,24,2} of size 576
   {3,2,24,4} of size 1152
   {3,2,24,4} of size 1152
   {3,2,24,4} of size 1152
   {3,2,24,4} of size 1152
   {3,2,24,6} of size 1728
   {3,2,24,6} of size 1728
   {3,2,24,6} of size 1728
   {3,2,24,3} of size 1728
Vertex Figure Of :
   {2,3,2,24} of size 576
   {3,3,2,24} of size 1152
   {4,3,2,24} of size 1152
   {6,3,2,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,12}*144
   3-fold quotients : {3,2,8}*96
   4-fold quotients : {3,2,6}*72
   6-fold quotients : {3,2,4}*48
   8-fold quotients : {3,2,3}*36
   12-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,48}*576, {6,2,24}*576
   3-fold covers : {3,2,72}*864, {9,2,24}*864, {3,6,24}*864a, {3,6,24}*864b
   4-fold covers : {3,2,96}*1152, {6,4,24}*1152a, {12,2,24}*1152, {6,2,48}*1152, {3,4,24}*1152
   5-fold covers : {15,2,24}*1440, {3,2,120}*1440
   6-fold covers : {3,2,144}*1728, {9,2,48}*1728, {3,6,48}*1728a, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {3,6,48}*1728b, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(22,25)(23,24)
(26,27);;
s3 := ( 4,10)( 5, 7)( 6,16)( 8,11)( 9,13)(12,22)(14,17)(15,19)(18,26)(20,23)
(21,24)(25,27);;
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, 
s0*s1*s0*s1*s0*s1, 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(27)!(2,3);
s1 := Sym(27)!(1,2);
s2 := Sym(27)!( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(22,25)
(23,24)(26,27);
s3 := Sym(27)!( 4,10)( 5, 7)( 6,16)( 8,11)( 9,13)(12,22)(14,17)(15,19)(18,26)
(20,23)(21,24)(25,27);
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, s0*s1*s0*s1*s0*s1, 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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