Polytope of Type {2,96}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,96}*384
if this polytope has a name.
Group : SmallGroup(384,1943)
Rank : 3
Schlafli Type : {2,96}
Number of vertices, edges, etc : 2, 96, 96
Order of s₀s₁s₂ : 96
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,96,2} of size 768
Vertex Figure Of :
   {2,2,96} of size 768
   {3,2,96} of size 1152
   {5,2,96} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,48}*192
   3-fold quotients : {2,32}*128
   4-fold quotients : {2,24}*96
   6-fold quotients : {2,16}*64
   8-fold quotients : {2,12}*48
   12-fold quotients : {2,8}*32
   16-fold quotients : {2,6}*24
   24-fold quotients : {2,4}*16
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,96}*768a, {2,192}*768
   3-fold covers : {2,288}*1152, {6,96}*1152b, {6,96}*1152c
   5-fold covers : {2,480}*1920, {10,96}*1920
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope