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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,12}*384a
if this polytope has a name.
Group : SmallGroup(384,18267)
Rank : 5
Schlafli Type : {2,2,4,12}
Number of vertices, edges, etc : 2, 2, 4, 24, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,12,2} of size 768
Vertex Figure Of :
   {2,2,2,4,12} of size 768
   {3,2,2,4,12} of size 1152
   {5,2,2,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
   3-fold quotients : {2,2,4,4}*128
   4-fold quotients : {2,2,2,6}*96
   6-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   8-fold quotients : {2,2,2,3}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,4,12}*768, {4,2,4,12}*768a, {2,2,8,12}*768a, {2,2,4,24}*768a, {2,2,8,12}*768b, {2,2,4,24}*768b, {2,2,4,12}*768a
   3-fold covers : {2,2,4,36}*1152a, {2,6,4,12}*1152, {6,2,4,12}*1152a, {2,2,12,12}*1152a, {2,2,12,12}*1152b
   5-fold covers : {2,2,4,60}*1920a, {2,10,4,12}*1920, {10,2,4,12}*1920a, {2,2,20,12}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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