Polytope of Type {2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,24}*768e
if this polytope has a name.
Group : SmallGroup(768,1089358)
Rank : 4
Schlafli Type : {2,4,24}
Number of vertices, edges, etc : 2, 8, 96, 48
Order of s₀s₁s₂s₃ : 6
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 : {2,4,12}*384c
   4-fold quotients : {2,4,6}*192
   8-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope