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Polytope of Type {24,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,2}*768b
if this polytope has a name.
Group : SmallGroup(768,323570)
Rank : 4
Schlafli Type : {24,4,2}
Number of vertices, edges, etc : 48, 96, 8, 2
Order of s0s1s2s3 : 12
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 : {12,4,2}*384a
   3-fold quotients : {8,4,2}*256b
   4-fold quotients : {12,4,2}*192a
   6-fold quotients : {4,4,2}*128
   8-fold quotients : {12,2,2}*96, {6,4,2}*96a
   12-fold quotients : {4,4,2}*64
   16-fold quotients : {6,2,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,73)( 2,75)( 3,74)( 4,76)( 5,78)( 6,77)( 7,79)( 8,81)( 9,80)(10,82)
(11,84)(12,83)(13,94)(14,96)(15,95)(16,91)(17,93)(18,92)(19,88)(20,90)(21,89)
(22,85)(23,87)(24,86)(25,49)(26,51)(27,50)(28,52)(29,54)(30,53)(31,55)(32,57)
(33,56)(34,58)(35,60)(36,59)(37,70)(38,72)(39,71)(40,67)(41,69)(42,68)(43,64)
(44,66)(45,65)(46,61)(47,63)(48,62);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)(21,24)
(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)(35,43)
(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,62)(64,65)(67,71)(68,70)(69,72)
(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)(83,91)
(84,93);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)
(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)
(22,46)(23,47)(24,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)
(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)
(68,92)(69,93)(70,94)(71,95)(72,96);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!( 1,73)( 2,75)( 3,74)( 4,76)( 5,78)( 6,77)( 7,79)( 8,81)( 9,80)
(10,82)(11,84)(12,83)(13,94)(14,96)(15,95)(16,91)(17,93)(18,92)(19,88)(20,90)
(21,89)(22,85)(23,87)(24,86)(25,49)(26,51)(27,50)(28,52)(29,54)(30,53)(31,55)
(32,57)(33,56)(34,58)(35,60)(36,59)(37,70)(38,72)(39,71)(40,67)(41,69)(42,68)
(43,64)(44,66)(45,65)(46,61)(47,63)(48,62);
s1 := Sym(98)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)
(21,24)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)
(35,43)(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,62)(64,65)(67,71)(68,70)
(69,72)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)
(83,91)(84,93);
s2 := Sym(98)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)
(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)
(21,45)(22,46)(23,47)(24,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)
(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)
(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1 >; 
 

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