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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,4}*768a
if this polytope has a name.
Group : SmallGroup(768,1036279)
Rank : 5
Schlafli Type : {2,6,4,4}
Number of vertices, edges, etc : 2, 6, 24, 16, 8
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 : {2,6,4,4}*384
   3-fold quotients : {2,2,4,4}*256
   4-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
   6-fold quotients : {2,2,4,4}*128
   8-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
   12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   16-fold quotients : {2,3,2,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope