Polytope of Type {96,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,2,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,34517)
Rank : 4
Schlafli Type : {96,2,3}
Number of vertices, edges, etc : 96, 96, 3, 3
Order of s₀s₁s₂s₃ : 96
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) :
   2-fold quotients : {48,2,3}*576
   3-fold quotients : {32,2,3}*384
   4-fold quotients : {24,2,3}*288
   6-fold quotients : {16,2,3}*192
   8-fold quotients : {12,2,3}*144
   12-fold quotients : {8,2,3}*96
   16-fold quotients : {6,2,3}*72
   24-fold quotients : {4,2,3}*48
   32-fold quotients : {3,2,3}*36
   48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)(17,24)
(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)
(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83)
(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)
(69,86)(70,88)(71,90)(72,89);;
s1 := ( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)(10,56)
(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)(21,63)
(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)(32,94)
(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)(43,83)
(44,82)(45,84)(46,80)(47,79)(48,81);;
s2 := (98,99);;
s3 := (97,98);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(99)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)
(17,24)(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)
(34,43)(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)
(57,83)(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)
(68,87)(69,86)(70,88)(71,90)(72,89);
s1 := Sym(99)!( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)
(10,56)(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)
(21,63)(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)
(32,94)(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)
(43,83)(44,82)(45,84)(46,80)(47,79)(48,81);
s2 := Sym(99)!(98,99);
s3 := Sym(99)!(97,98);
poly := sub<Sym(99)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope