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Polytope of Type {2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,24}*768d
if this polytope has a name.
Group : SmallGroup(768,1089137)
Rank : 4
Schlafli Type : {2,4,24}
Number of vertices, edges, etc : 2, 8, 96, 48
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 : {2,4,12}*384b
   4-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   8-fold quotients : {2,2,12}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32
   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, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)
(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)
(44,46)(47,49)(48,50)(51,65)(52,66)(53,63)(54,64)(55,69)(56,70)(57,67)(58,68)
(59,73)(60,74)(61,71)(62,72)(75,89)(76,90)(77,87)(78,88)(79,93)(80,94)(81,91)
(82,92)(83,97)(84,98)(85,95)(86,96);;
s2 := ( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)(12,57)
(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)(23,67)
(24,69)(25,68)(26,70)(27,87)(28,89)(29,88)(30,90)(31,95)(32,97)(33,96)(34,98)
(35,91)(36,93)(37,92)(38,94)(39,75)(40,77)(41,76)(42,78)(43,83)(44,85)(45,84)
(46,86)(47,79)(48,81)(49,80)(50,82);;
s3 := ( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)(20,22)
(27,47)(28,50)(29,49)(30,48)(31,43)(32,46)(33,45)(34,44)(35,39)(36,42)(37,41)
(38,40)(51,83)(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)(60,78)
(61,77)(62,76)(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)(71,87)
(72,90)(73,89)(74,88);;
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, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)
(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)
(43,45)(44,46)(47,49)(48,50)(51,65)(52,66)(53,63)(54,64)(55,69)(56,70)(57,67)
(58,68)(59,73)(60,74)(61,71)(62,72)(75,89)(76,90)(77,87)(78,88)(79,93)(80,94)
(81,91)(82,92)(83,97)(84,98)(85,95)(86,96);
s2 := Sym(98)!( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)
(12,57)(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)
(23,67)(24,69)(25,68)(26,70)(27,87)(28,89)(29,88)(30,90)(31,95)(32,97)(33,96)
(34,98)(35,91)(36,93)(37,92)(38,94)(39,75)(40,77)(41,76)(42,78)(43,83)(44,85)
(45,84)(46,86)(47,79)(48,81)(49,80)(50,82);
s3 := Sym(98)!( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)
(20,22)(27,47)(28,50)(29,49)(30,48)(31,43)(32,46)(33,45)(34,44)(35,39)(36,42)
(37,41)(38,40)(51,83)(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)
(60,78)(61,77)(62,76)(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)
(71,87)(72,90)(73,89)(74,88);
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, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 >; 
 

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