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Polytope of Type {12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2}*384b
if this polytope has a name.
Group : SmallGroup(384,20049)
Rank : 4
Schlafli Type : {12,4,2}
Number of vertices, edges, etc : 24, 48, 8, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,4,2,2} of size 768
   {12,4,2,3} of size 1152
   {12,4,2,5} of size 1920
Vertex Figure Of :
   {2,12,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4,2}*192b, {12,4,2}*192c, {6,4,2}*192
   4-fold quotients : {12,2,2}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   8-fold quotients : {3,4,2}*48, {6,2,2}*48
   12-fold quotients : {4,2,2}*32
   16-fold quotients : {3,2,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2}*768d, {12,4,4}*768e, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d
   3-fold covers : {36,4,2}*1152b, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e
   5-fold covers : {12,4,10}*1920b, {12,20,2}*1920b, {60,4,2}*1920b
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)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)
(73,85)(74,87)(75,86)(76,88)(77,93)(78,95)(79,94)(80,96)(81,89)(82,91)(83,90)
(84,92);;
s1 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,25)( 6,26)( 7,28)( 8,27)( 9,33)(10,34)
(11,36)(12,35)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)(21,45)
(22,46)(23,48)(24,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)
(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)
(68,87)(69,93)(70,94)(71,96)(72,95);;
s2 := ( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)
(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)
(22,71)(23,70)(24,69)(25,76)(26,75)(27,74)(28,73)(29,80)(30,79)(31,78)(32,77)
(33,84)(34,83)(35,82)(36,81)(37,88)(38,87)(39,86)(40,85)(41,92)(42,91)(43,90)
(44,89)(45,96)(46,95)(47,94)(48,93);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)
(68,72)(73,85)(74,87)(75,86)(76,88)(77,93)(78,95)(79,94)(80,96)(81,89)(82,91)
(83,90)(84,92);
s1 := Sym(98)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,25)( 6,26)( 7,28)( 8,27)( 9,33)
(10,34)(11,36)(12,35)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)
(21,45)(22,46)(23,48)(24,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)
(56,75)(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)
(67,88)(68,87)(69,93)(70,94)(71,96)(72,95);
s2 := Sym(98)!( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)
(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)
(21,72)(22,71)(23,70)(24,69)(25,76)(26,75)(27,74)(28,73)(29,80)(30,79)(31,78)
(32,77)(33,84)(34,83)(35,82)(36,81)(37,88)(38,87)(39,86)(40,85)(41,92)(42,91)
(43,90)(44,89)(45,96)(46,95)(47,94)(48,93);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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