Polytope of Type {24,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 4
Schlafli Type : {24,6,2}
Number of vertices, edges, etc : 32, 96, 8, 2
Order of s₀s₁s₂s₃ : 8
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 : {12,6,2}*384a
   4-fold quotients : {6,6,2}*192
   8-fold quotients : {3,6,2}*96, {6,3,2}*96
   12-fold quotients : {8,2,2}*64
   16-fold quotients : {3,3,2}*48
   24-fold quotients : {4,2,2}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope