Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*288c
if this polytope has a name.
Group : SmallGroup(288,977)
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
   {6,12,6,2} of size 1728
   {3,12,6,2} of size 1728
   {6,12,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,2}*144b
   3-fold quotients : {4,6,2}*96a
   4-fold quotients : {6,3,2}*72
   6-fold quotients : {2,6,2}*48
   9-fold quotients : {4,2,2}*32
   12-fold quotients : {2,3,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12,2}*576b, {24,6,2}*576c, {12,6,4}*576c
   3-fold covers : {12,18,2}*864b, {12,6,2}*864c, {12,6,2}*864g, {12,6,6}*864f, {12,6,6}*864g
   4-fold covers : {12,12,4}*1152a, {12,24,2}*1152b, {24,12,2}*1152c, {12,24,2}*1152e, {24,12,2}*1152f, {12,12,2}*1152b, {12,6,8}*1152a, {24,6,4}*1152a, {48,6,2}*1152a, {12,6,4}*1152d, {12,6,2}*1152e, {12,6,2}*1152f
   5-fold covers : {60,6,2}*1440a, {12,6,10}*1440c, {12,30,2}*1440c
   6-fold covers : {12,36,2}*1728b, {12,12,2}*1728b, {24,18,2}*1728b, {12,18,4}*1728b, {24,6,2}*1728c, {12,6,4}*1728c, {24,6,2}*1728f, {12,6,12}*1728c, {12,12,6}*1728c, {12,12,6}*1728e, {24,6,6}*1728f, {24,6,6}*1728g, {12,12,2}*1728h, {12,6,12}*1728g, {12,6,4}*1728h
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope