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Polytope of Type {4,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*288a
Also Known As : {{4,6|2},{6,6|2}}. if this polytope has another 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
   {4,6,6,3} of size 1152
   {4,6,6,4} of size 1152
   {4,6,6,6} of size 1728
   {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}*144a
   3-fold quotients : {4,2,6}*96, {4,6,2}*96a
   6-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
   9-fold quotients : {4,2,2}*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, {4,6,12}*576a, {8,6,6}*576a
   3-fold covers : {4,6,18}*864a, {4,18,6}*864a, {4,6,6}*864b, {12,6,6}*864b, {4,6,6}*864h, {12,6,6}*864f
   4-fold covers : {4,12,12}*1152b, {8,12,6}*1152b, {4,24,6}*1152c, {8,12,6}*1152e, {4,24,6}*1152f, {4,12,6}*1152b, {8,6,12}*1152b, {4,6,24}*1152b, {16,6,6}*1152a, {4,6,6}*1152d, {4,6,12}*1152b, {4,12,6}*1152g
   5-fold covers : {20,6,6}*1440a, {4,6,30}*1440b, {4,30,6}*1440b
   6-fold covers : {4,6,36}*1728a, {4,18,12}*1728a, {4,12,18}*1728a, {4,36,6}*1728a, {4,6,12}*1728a, {4,12,6}*1728b, {8,6,18}*1728a, {8,18,6}*1728a, {8,6,6}*1728b, {24,6,6}*1728b, {12,6,12}*1728b, {12,6,12}*1728c, {12,12,6}*1728b, {12,12,6}*1728c, {8,6,6}*1728e, {24,6,6}*1728f, {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)( 2,20)( 3,21)( 4,25)( 5,26)( 6,27)( 7,22)( 8,23)( 9,24)(10,28)
(11,29)(12,30)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18)(19,22)(20,24)
(21,23)(26,27)(28,31)(29,33)(30,32)(35,36);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35);;
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, 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 ];;
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)( 2,20)( 3,21)( 4,25)( 5,26)( 6,27)( 7,22)( 8,23)( 9,24)
(10,28)(11,29)(12,30)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33);
s2 := Sym(36)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18)(19,22)
(20,24)(21,23)(26,27)(28,31)(29,33)(30,32)(35,36);
s3 := Sym(36)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35);
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, 
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 >; 
 
References : None.
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