Polytope of Type {4,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,2}*768d
if this polytope has a name.
Group : SmallGroup(768,1089137)
Rank : 4
Schlafli Type : {4,24,2}
Number of vertices, edges, etc : 8, 96, 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) :
   2-fold quotients : {4,12,2}*384b
   4-fold quotients : {4,12,2}*192b, {4,12,2}*192c, {4,6,2}*192
   8-fold quotients : {2,12,2}*96, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   16-fold quotients : {4,3,2}*48, {2,6,2}*48
   24-fold quotients : {2,4,2}*32
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope