Polytope of Type {6,4,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1036279)
Rank : 5
Schlafli Type : {6,4,4,2}
Number of vertices, edges, etc : 6, 24, 16, 8, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,4,2}*384
   3-fold quotients : {2,4,4,2}*256
   4-fold quotients : {6,2,4,2}*192, {6,4,2,2}*192a
   6-fold quotients : {2,4,4,2}*128
   8-fold quotients : {3,2,4,2}*96, {6,2,2,2}*96
   12-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   16-fold quotients : {3,2,2,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s4 := (25,26);;
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*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, 
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(26)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24);
s1 := Sym(26)!( 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(26)!(19,22)(20,23)(21,24);
s3 := Sym(26)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,19)(14,20)(15,21)
(16,22)(17,23)(18,24);
s4 := Sym(26)!(25,26);
poly := sub<Sym(26)|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*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, 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 >;

to this polytope