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Polytope of Type {4,12,2}

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

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