Polytope of Type {4,6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,2}*576a
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 5
Schlafli Type : {4,6,6,2}
Number of vertices, edges, etc : 4, 12, 18, 6, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,6,2,2} of size 1152
   {4,6,6,2,3} of size 1728
Vertex Figure Of :
   {2,4,6,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6,2}*288a
   3-fold quotients : {4,2,6,2}*192, {4,6,2,2}*192a
   6-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96, {2,6,2,2}*96
   9-fold quotients : {4,2,2,2}*64
   12-fold quotients : {2,2,3,2}*48, {2,3,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,6,2}*1152a, {4,6,6,4}*1152a, {4,6,12,2}*1152b, {8,6,6,2}*1152a
   3-fold covers : {4,6,18,2}*1728a, {4,18,6,2}*1728a, {4,6,6,2}*1728b, {12,6,6,2}*1728b, {4,6,6,6}*1728d, {4,6,6,6}*1728e, {4,6,6,2}*1728h, {12,6,6,2}*1728f
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);;
s4 := (37,38);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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(38)!(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36);
s1 := Sym(38)!( 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(38)!( 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(38)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35);
s4 := Sym(38)!(37,38);
poly := sub<Sym(38)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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 >;

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