Polytope of Type {6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4}*384a
Also Known As : {{6,4|2},{4,4}₄}. if this polytope has another name.
Group : SmallGroup(384,12882)
Rank : 4
Schlafli Type : {6,4,4}
Number of vertices, edges, etc : 6, 24, 16, 8
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,4,2} of size 768
   {6,4,4,3} of size 1152
Vertex Figure Of :
   {2,6,4,4} of size 768
   {3,6,4,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,4}*192
   3-fold quotients : {2,4,4}*128
   4-fold quotients : {6,2,4}*96, {6,4,2}*96a
   6-fold quotients : {2,4,4}*64
   8-fold quotients : {3,2,4}*48, {6,2,2}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {3,2,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,4,8}*768a, {6,8,4}*768a, {12,4,4}*768a, {6,4,4}*768a, {6,4,8}*768b, {6,8,4}*768b
   3-fold covers : {18,4,4}*1152a, {6,4,12}*1152a, {6,12,4}*1152b, {6,12,4}*1152c
   5-fold covers : {30,4,4}*1920a, {6,4,20}*1920a, {6,20,4}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope