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Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*288b
if this polytope has a name.
Group : SmallGroup(288,951)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 12, 36, 6, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,6,2,2} of size 576
   {12,6,2,3} of size 864
   {12,6,2,4} of size 1152
   {12,6,2,5} of size 1440
   {12,6,2,6} of size 1728
Vertex Figure Of :
   {2,12,6,2} of size 576
   {4,12,6,2} of size 1152
   {4,12,6,2} of size 1152
   {4,12,6,2} of size 1152
   {6,12,6,2} of size 1728
   {6,12,6,2} of size 1728
   {6,12,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,2}*144c
   3-fold quotients : {12,2,2}*96
   4-fold quotients : {3,6,2}*72
   6-fold quotients : {6,2,2}*48
   9-fold quotients : {4,2,2}*32
   12-fold quotients : {3,2,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,6,2}*576b, {12,12,2}*576c, {12,6,4}*576b
   3-fold covers : {36,6,2}*864b, {12,6,2}*864a, {12,6,6}*864d, {12,6,2}*864g
   4-fold covers : {12,12,4}*1152c, {24,12,2}*1152b, {12,24,2}*1152c, {24,12,2}*1152e, {12,24,2}*1152f, {12,12,2}*1152c, {12,6,8}*1152c, {24,6,4}*1152c, {48,6,2}*1152c, {12,12,2}*1152e, {12,6,2}*1152a
   5-fold covers : {12,6,10}*1440b, {12,30,2}*1440a, {60,6,2}*1440c
   6-fold covers : {72,6,2}*1728b, {24,6,2}*1728a, {36,12,2}*1728b, {36,6,4}*1728b, {12,12,2}*1728a, {12,6,4}*1728b, {24,6,6}*1728d, {24,6,2}*1728f, {12,6,12}*1728f, {12,12,6}*1728f, {12,12,2}*1728h, {12,6,4}*1728h
Permutation Representation (GAP) :
s0 := ( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)
(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)(21,65)
(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)
(33,62)(34,58)(35,60)(36,59);;
s1 := ( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)(10,68)
(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)(21,42)
(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)
(33,48)(34,53)(35,52)(36,54);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s3 := (73,74);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 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(74)!( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)
(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)
(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)
(32,63)(33,62)(34,58)(35,60)(36,59);
s1 := Sym(74)!( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)
(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)
(21,42)(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)
(32,46)(33,48)(34,53)(35,52)(36,54);
s2 := Sym(74)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
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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