Polytope of Type {4,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*288b
if this polytope has a name.
Group : SmallGroup(288,958)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 4, 12, 18, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,6,2} of size 576
   {4,6,6,3} of size 864
   {4,6,6,4} of size 1152
   {4,6,6,6} of size 1728
   {4,6,6,6} of size 1728
Vertex Figure Of :
   {2,4,6,6} of size 576
   {4,4,6,6} of size 1152
   {6,4,6,6} of size 1728
   {3,4,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6}*144c
   3-fold quotients : {4,6,2}*96a
   4-fold quotients : {2,3,6}*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 : {4,12,6}*576b, {8,6,6}*576b, {4,6,12}*576c
   3-fold covers : {4,18,6}*864b, {4,6,6}*864a, {12,6,6}*864c, {4,6,6}*864h, {12,6,6}*864g
   4-fold covers : {4,12,12}*1152a, {8,12,6}*1152a, {4,24,6}*1152b, {8,12,6}*1152d, {4,24,6}*1152e, {4,12,6}*1152a, {8,6,12}*1152a, {4,6,24}*1152a, {16,6,6}*1152b, {4,6,6}*1152c, {4,6,6}*1152e, {4,6,12}*1152c
   5-fold covers : {20,6,6}*1440b, {4,6,30}*1440a, {4,30,6}*1440c
   6-fold covers : {4,36,6}*1728b, {4,12,6}*1728a, {8,18,6}*1728b, {8,6,6}*1728a, {4,18,12}*1728b, {4,6,12}*1728c, {24,6,6}*1728c, {12,6,12}*1728d, {12,12,6}*1728d, {12,12,6}*1728e, {8,6,6}*1728e, {24,6,6}*1728g, {12,6,12}*1728g, {4,12,6}*1728j, {4,6,12}*1728h
Permutation Representation (GAP) :

s0 := (19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36);;
s1 := ( 1,19)( 2,21)( 3,20)( 4,25)( 5,27)( 6,26)( 7,22)( 8,24)( 9,23)(10,28)
(11,30)(12,29)(13,34)(14,36)(15,35)(16,31)(17,33)(18,32);;
s2 := ( 1, 5)( 2, 4)( 3, 6)( 7, 8)(10,14)(11,13)(12,15)(16,17)(19,23)(20,22)
(21,24)(25,26)(28,32)(29,31)(30,33)(34,35);;
s3 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)
(32,35)(33,36);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36);
s1 := Sym(36)!( 1,19)( 2,21)( 3,20)( 4,25)( 5,27)( 6,26)( 7,22)( 8,24)( 9,23)
(10,28)(11,30)(12,29)(13,34)(14,36)(15,35)(16,31)(17,33)(18,32);
s2 := Sym(36)!( 1, 5)( 2, 4)( 3, 6)( 7, 8)(10,14)(11,13)(12,15)(16,17)(19,23)
(20,22)(21,24)(25,26)(28,32)(29,31)(30,33)(34,35);
s3 := Sym(36)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)
(31,34)(32,35)(33,36);
poly := sub<Sym(36)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 >;

References : None.
to this polytope