Polytope of Type {6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*288c
if this polytope has a name.
Group : SmallGroup(288,977)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 6, 36, 12, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,2,2} of size 576
   {6,12,2,3} of size 864
   {6,12,2,4} of size 1152
   {6,12,2,5} of size 1440
   {6,12,2,6} of size 1728
Vertex Figure Of :
   {2,6,12,2} of size 576
   {4,6,12,2} of size 1152
   {4,6,12,2} of size 1152
   {6,6,12,2} of size 1728
   {6,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,2}*144c
   3-fold quotients : {6,4,2}*96a
   4-fold quotients : {3,6,2}*72
   6-fold quotients : {6,2,2}*48
   9-fold quotients : {2,4,2}*32
   12-fold quotients : {3,2,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12,2}*576c, {6,24,2}*576c, {6,12,4}*576c
   3-fold covers : {18,12,2}*864b, {6,12,2}*864c, {6,12,2}*864g, {6,12,6}*864f
   4-fold covers : {12,12,4}*1152c, {6,12,8}*1152c, {6,24,4}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {6,12,8}*1152f, {6,24,4}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {6,12,4}*1152c, {12,12,2}*1152c, {6,48,2}*1152a, {6,12,2}*1152e, {6,12,2}*1152f
   5-fold covers : {6,60,2}*1440a, {6,12,10}*1440c, {30,12,2}*1440c
   6-fold covers : {36,12,2}*1728b, {12,12,2}*1728a, {18,24,2}*1728b, {6,24,2}*1728c, {18,12,4}*1728b, {6,12,4}*1728c, {6,24,2}*1728f, {12,12,6}*1728f, {6,24,6}*1728g, {12,12,2}*1728h, {6,12,4}*1728j, {6,12,12}*1728g
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)(19,55)(20,57)(21,56)
(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)
(33,71)(34,67)(35,69)(36,68);;
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)(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);;
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*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)(19,55)(20,57)
(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)
(32,72)(33,71)(34,67)(35,69)(36,68);
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)(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);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope