Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*288a
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
   {2,6,12,3} of size 1152
   {2,6,12,6} of size 1728
   {2,6,12,6} of size 1728
   {2,6,12,6} of size 1728
   {2,6,12,3} 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}*144a
   3-fold quotients : {2,2,12}*96, {2,6,4}*96a
   6-fold quotients : {2,2,6}*48, {2,6,2}*48
   9-fold quotients : {2,2,4}*32
   12-fold quotients : {2,2,3}*24, {2,3,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,12}*576a, {2,6,24}*576a, {2,12,12}*576a
   3-fold covers : {2,6,36}*864a, {2,18,12}*864a, {2,6,12}*864b, {6,6,12}*864b, {6,6,12}*864d, {2,6,12}*864g
   4-fold covers : {4,12,12}*1152b, {2,12,24}*1152a, {2,24,12}*1152a, {2,12,24}*1152d, {2,24,12}*1152d, {2,12,12}*1152a, {8,6,12}*1152b, {4,6,24}*1152b, {2,6,48}*1152b, {2,12,12}*1152f, {4,6,12}*1152a, {2,6,12}*1152b
   5-fold covers : {10,6,12}*1440a, {2,30,12}*1440b, {2,6,60}*1440b
   6-fold covers : {4,6,36}*1728a, {4,18,12}*1728a, {4,6,12}*1728a, {2,6,72}*1728a, {2,18,24}*1728a, {2,6,24}*1728b, {2,12,36}*1728a, {2,36,12}*1728a, {2,12,12}*1728c, {6,6,24}*1728b, {6,6,24}*1728d, {2,6,24}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {6,12,12}*1728b, {6,12,12}*1728d, {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)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)(12,69)
(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)(23,44)
(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)(34,49)
(35,50)(36,54)(37,55)(38,56);;
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, 
s1*s2*s3*s2*s1*s2*s3*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)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)
(12,69)(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)
(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)
(34,49)(35,50)(36,54)(37,55)(38,56);
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, s1*s2*s3*s2*s1*s2*s3*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 >;

to this polytope