Polytope of Type {6,3,2}

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

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

Permutation Representation (Magma) :

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

to this polytope