Polytope of Type {2,4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,2}*384a
if this polytope has a name.
Group : SmallGroup(384,18267)
Rank : 5
Schlafli Type : {2,4,12,2}
Number of vertices, edges, etc : 2, 4, 24, 12, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,12,2,2} of size 768
   {2,4,12,2,3} of size 1152
   {2,4,12,2,5} of size 1920
Vertex Figure Of :
   {2,2,4,12,2} of size 768
   {3,2,4,12,2} of size 1152
   {5,2,4,12,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,12,2}*192, {2,4,6,2}*192a
   3-fold quotients : {2,4,4,2}*128
   4-fold quotients : {2,2,6,2}*96
   6-fold quotients : {2,2,4,2}*64, {2,4,2,2}*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 : {4,4,12,2}*768, {2,4,12,4}*768a, {2,8,12,2}*768a, {2,4,24,2}*768a, {2,8,12,2}*768b, {2,4,24,2}*768b, {2,4,12,2}*768a
   3-fold covers : {2,4,36,2}*1152a, {2,4,12,6}*1152a, {2,4,12,6}*1152b, {6,4,12,2}*1152, {2,12,12,2}*1152a, {2,12,12,2}*1152b
   5-fold covers : {2,4,60,2}*1920a, {2,4,12,10}*1920a, {10,4,12,2}*1920, {2,20,12,2}*1920
Permutation Representation (GAP) :

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