Polytope of Type {2,2,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,24,2}*384
if this polytope has a name.
Group : SmallGroup(384,19724)
Rank : 5
Schlafli Type : {2,2,24,2}
Number of vertices, edges, etc : 2, 2, 24, 24, 2
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,24,2,2} of size 768
   {2,2,24,2,3} of size 1152
   {2,2,24,2,5} of size 1920
Vertex Figure Of :
   {2,2,2,24,2} of size 768
   {3,2,2,24,2} of size 1152
   {5,2,2,24,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,12,2}*192
   3-fold quotients : {2,2,8,2}*128
   4-fold quotients : {2,2,6,2}*96
   6-fold quotients : {2,2,4,2}*64
   8-fold quotients : {2,2,3,2}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,24,4}*768a, {2,4,24,2}*768a, {4,2,24,2}*768, {2,2,48,2}*768
   3-fold covers : {2,2,72,2}*1152, {2,2,24,6}*1152b, {2,2,24,6}*1152c, {2,6,24,2}*1152b, {2,6,24,2}*1152c, {6,2,24,2}*1152
   5-fold covers : {2,2,120,2}*1920, {2,2,24,10}*1920, {2,10,24,2}*1920, {10,2,24,2}*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);;
s4 := (29,30);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(30)!(1,2);
s1 := Sym(30)!(3,4);
s2 := Sym(30)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,26)
(24,25)(27,28);
s3 := Sym(30)!( 5,11)( 6, 8)( 7,17)( 9,12)(10,14)(13,23)(15,18)(16,20)(19,27)
(21,24)(22,25)(26,28);
s4 := Sym(30)!(29,30);
poly := sub<Sym(30)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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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