Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*288a
if this polytope has a name.
Group : SmallGroup(288,951)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 12, 36, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,6,2} of size 576
   {2,12,6,3} of size 864
   {2,12,6,4} of size 1152
   {2,12,6,3} of size 1152
   {2,12,6,4} of size 1152
   {2,12,6,6} of size 1728
   {2,12,6,6} of size 1728
   {2,12,6,6} of size 1728
Vertex Figure Of :
   {2,2,12,6} of size 576
   {3,2,12,6} of size 864
   {4,2,12,6} of size 1152
   {5,2,12,6} of size 1440
   {6,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6}*144a
   3-fold quotients : {2,12,2}*96, {2,4,6}*96a
   6-fold quotients : {2,2,6}*48, {2,6,2}*48
   9-fold quotients : {2,4,2}*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 : {4,12,6}*576a, {2,24,6}*576a, {2,12,12}*576a
   3-fold covers : {2,36,6}*864a, {2,12,18}*864a, {2,12,6}*864b, {6,12,6}*864b, {6,12,6}*864c, {2,12,6}*864g
   4-fold covers : {4,12,12}*1152b, {8,12,6}*1152b, {4,24,6}*1152c, {2,12,24}*1152a, {2,24,12}*1152a, {8,12,6}*1152e, {4,24,6}*1152f, {2,12,24}*1152d, {2,24,12}*1152d, {4,12,6}*1152b, {2,12,12}*1152a, {2,48,6}*1152b, {4,12,6}*1152e, {2,12,12}*1152d, {2,12,6}*1152b
   5-fold covers : {10,12,6}*1440a, {2,12,30}*1440b, {2,60,6}*1440b
   6-fold covers : {4,12,18}*1728a, {4,36,6}*1728a, {4,12,6}*1728b, {2,72,6}*1728a, {2,24,18}*1728a, {2,24,6}*1728b, {2,12,36}*1728a, {2,36,12}*1728a, {2,12,12}*1728c, {6,24,6}*1728b, {6,24,6}*1728c, {2,24,6}*1728f, {6,12,12}*1728b, {6,12,12}*1728d, {12,12,6}*1728b, {12,12,6}*1728c, {2,12,12}*1728h, {4,12,6}*1728j
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,39)( 4,40)( 5,41)( 6,45)( 7,46)( 8,47)( 9,42)(10,43)(11,44)(12,48)
(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,66)(22,67)(23,68)
(24,72)(25,73)(26,74)(27,69)(28,70)(29,71)(30,57)(31,58)(32,59)(33,63)(34,64)
(35,65)(36,60)(37,61)(38,62);;
s2 := ( 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);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)
(66,67)(69,70)(72,73);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(74)!(1,2);
s1 := Sym(74)!( 3,39)( 4,40)( 5,41)( 6,45)( 7,46)( 8,47)( 9,42)(10,43)(11,44)
(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,66)(22,67)
(23,68)(24,72)(25,73)(26,74)(27,69)(28,70)(29,71)(30,57)(31,58)(32,59)(33,63)
(34,64)(35,65)(36,60)(37,61)(38,62);
s2 := 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);
s3 := Sym(74)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)
(63,64)(66,67)(69,70)(72,73);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope