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Polytope of Type {12,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,2}*384a
if this polytope has a name.
Group : SmallGroup(384,11319)
Rank : 4
Schlafli Type : {12,8,2}
Number of vertices, edges, etc : 12, 48, 8, 2
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,8,2,2} of size 768
   {12,8,2,3} of size 1152
   {12,8,2,5} of size 1920
Vertex Figure Of :
   {2,12,8,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4,2}*192a, {6,8,2}*192
   3-fold quotients : {4,8,2}*128a
   4-fold quotients : {12,2,2}*96, {6,4,2}*96a
   6-fold quotients : {4,4,2}*64, {2,8,2}*64
   8-fold quotients : {6,2,2}*48
   12-fold quotients : {2,4,2}*32, {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 : {12,8,2}*768a, {24,8,2}*768a, {24,8,2}*768c, {12,8,4}*768d, {12,16,2}*768a, {12,16,2}*768b
   3-fold covers : {36,8,2}*1152a, {12,8,6}*1152a, {12,24,2}*1152a, {12,24,2}*1152c
   5-fold covers : {60,8,2}*1920a, {12,8,10}*1920a, {12,40,2}*1920a
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(25,37)(26,39)
(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47)(50,51)
(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(73,85)(74,87)(75,86)(76,88)
(77,90)(78,89)(79,91)(80,93)(81,92)(82,94)(83,96)(84,95);;
s1 := ( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,35)( 8,34)( 9,36)(10,32)
(11,31)(12,33)(13,38)(14,37)(15,39)(16,41)(17,40)(18,42)(19,47)(20,46)(21,48)
(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,83)(56,82)
(57,84)(58,80)(59,79)(60,81)(61,86)(62,85)(63,87)(64,89)(65,88)(66,90)(67,95)
(68,94)(69,96)(70,92)(71,91)(72,93);;
s2 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)(10,55)
(11,56)(12,57)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,70)(20,71)(21,72)
(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(25,37)
(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47)
(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(73,85)(74,87)(75,86)
(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,94)(83,96)(84,95);
s1 := Sym(98)!( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,35)( 8,34)( 9,36)
(10,32)(11,31)(12,33)(13,38)(14,37)(15,39)(16,41)(17,40)(18,42)(19,47)(20,46)
(21,48)(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,83)
(56,82)(57,84)(58,80)(59,79)(60,81)(61,86)(62,85)(63,87)(64,89)(65,88)(66,90)
(67,95)(68,94)(69,96)(70,92)(71,91)(72,93);
s2 := Sym(98)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)
(10,55)(11,56)(12,57)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,70)(20,71)
(21,72)(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)
(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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