Polytope of Type {2,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {2,6,3}
Number of vertices, edges, etc : 2, 96, 144, 48
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,6,3}*384
   4-fold quotients : {2,6,3}*288
   12-fold quotients : {2,6,3}*96
   16-fold quotients : {2,6,3}*72
   24-fold quotients : {2,3,3}*48
   48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope