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Polytope of Type {2,6,12}

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

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