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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}*384a
if this polytope has a name.
Group : SmallGroup(384,11182)
Rank : 4
Schlafli Type : {2,4,24}
Number of vertices, edges, etc : 2, 4, 48, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,24,2} of size 768
Vertex Figure Of :
   {2,2,4,24} of size 768
   {3,2,4,24} of size 1152
   {5,2,4,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,12}*192a, {2,2,24}*192
   3-fold quotients : {2,4,8}*128a
   4-fold quotients : {2,2,12}*96, {2,4,6}*96a
   6-fold quotients : {2,4,4}*64, {2,2,8}*64
   8-fold quotients : {2,2,6}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,2,3}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,24}*768a, {2,8,24}*768b, {2,8,24}*768c, {4,4,24}*768a, {2,4,48}*768a, {2,4,48}*768b
   3-fold covers : {2,4,72}*1152a, {6,4,24}*1152a, {2,12,24}*1152a, {2,12,24}*1152b
   5-fold covers : {2,4,120}*1920a, {10,4,24}*1920a, {2,20,24}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)
(24,72)(25,73)(26,74)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)
(46,88)(47,89)(48,90)(49,91)(50,92);;
s2 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)
(13,38)(14,37)(15,42)(16,44)(17,43)(18,39)(19,41)(20,40)(21,48)(22,50)(23,49)
(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)
(59,82)(60,84)(61,86)(62,85)(63,90)(64,92)(65,91)(66,87)(67,89)(68,88)(69,96)
(70,98)(71,97)(72,93)(73,95)(74,94);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,19)(16,18)(17,20)(21,25)(22,24)(23,26)
(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)(35,47)(36,49)(37,48)
(38,50)(51,52)(54,55)(57,58)(60,61)(63,67)(64,66)(65,68)(69,73)(70,72)(71,74)
(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,94)(82,93)(83,95)(84,97)(85,96)
(86,98);;
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*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)
(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)
(23,71)(24,72)(25,73)(26,74)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)
(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)
(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);
s2 := Sym(98)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)
(12,36)(13,38)(14,37)(15,42)(16,44)(17,43)(18,39)(19,41)(20,40)(21,48)(22,50)
(23,49)(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)
(58,83)(59,82)(60,84)(61,86)(62,85)(63,90)(64,92)(65,91)(66,87)(67,89)(68,88)
(69,96)(70,98)(71,97)(72,93)(73,95)(74,94);
s3 := Sym(98)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,19)(16,18)(17,20)(21,25)(22,24)
(23,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)(35,47)(36,49)
(37,48)(38,50)(51,52)(54,55)(57,58)(60,61)(63,67)(64,66)(65,68)(69,73)(70,72)
(71,74)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,94)(82,93)(83,95)(84,97)
(85,96)(86,98);
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*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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