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

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

Permutation Representation (Magma) :

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

to this polytope