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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,2,2}*768
if this polytope has a name.
Group : SmallGroup(768,1076197)
Rank : 6
Schlafli Type : {4,4,6,2,2}
Number of vertices, edges, etc : 4, 8, 12, 6, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {2,4,6,2,2}*384a, {4,2,6,2,2}*384
   3-fold quotients : {4,4,2,2,2}*256
   4-fold quotients : {4,2,3,2,2}*192, {2,2,6,2,2}*192
   6-fold quotients : {2,4,2,2,2}*128, {4,2,2,2,2}*128
   8-fold quotients : {2,2,3,2,2}*96
   12-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)
(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)
(34,46)(35,47)(36,48);;
s1 := (13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,28)(26,29)(27,30)(31,34)
(32,35)(33,36)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45);;
s2 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)
(11,36)(12,35)(13,37)(14,39)(15,38)(16,40)(17,42)(18,41)(19,43)(20,45)(21,44)
(22,46)(23,48)(24,47);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);;
s4 := (49,50);;
s5 := (51,52);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)
(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)
(33,45)(34,46)(35,47)(36,48);
s1 := Sym(52)!(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,28)(26,29)(27,30)
(31,34)(32,35)(33,36)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45);
s2 := Sym(52)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)
(10,34)(11,36)(12,35)(13,37)(14,39)(15,38)(16,40)(17,42)(18,41)(19,43)(20,45)
(21,44)(22,46)(23,48)(24,47);
s3 := Sym(52)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);
s4 := Sym(52)!(49,50);
s5 := Sym(52)!(51,52);
poly := sub<Sym(52)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >;

to this polytope