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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,4,4}*768
if this polytope has a name.
Group : SmallGroup(768,1076197)
Rank : 6
Schlafli Type : {2,2,6,4,4}
Number of vertices, edges, etc : 2, 2, 6, 12, 8, 4
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 : {2,2,6,2,4}*384, {2,2,6,4,2}*384a
   3-fold quotients : {2,2,2,4,4}*256
   4-fold quotients : {2,2,3,2,4}*192, {2,2,6,2,2}*192
   6-fold quotients : {2,2,2,2,4}*128, {2,2,2,4,2}*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 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(51,52);;
s3 := ( 5,18)( 6,17)( 7,19)( 8,21)( 9,20)(10,22)(11,24)(12,23)(13,25)(14,27)
(15,26)(16,28)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47)(37,49)
(38,51)(39,50)(40,52);;
s4 := (17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,33)(31,34)(35,38)
(36,39)(37,40)(41,50)(42,51)(43,52)(44,47)(45,48)(46,49);;
s5 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,37)(14,38)
(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)
(26,50)(27,51)(28,52);;
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*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope