Polytope of Type {2,6,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3,6}*432
if this polytope has a name.
Group : SmallGroup(432,759)
Rank : 5
Schlafli Type : {2,6,3,6}
Number of vertices, edges, etc : 2, 6, 9, 9, 6
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,3,6,2} of size 864
   {2,6,3,6,3} of size 1296
   {2,6,3,6,4} of size 1728
Vertex Figure Of :
   {2,2,6,3,6} of size 864
   {3,2,6,3,6} of size 1296
   {4,2,6,3,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,3,6}*144, {2,6,3,2}*144
   9-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,3,6}*864, {2,6,6,6}*864f
   3-fold covers : {2,6,9,6}*1296, {2,6,3,6}*1296a, {2,6,3,6}*1296b, {6,6,3,6}*1296b
   4-fold covers : {8,6,3,6}*1728, {2,6,12,6}*1728e, {4,6,6,6}*1728h, {2,6,6,12}*1728g, {2,12,6,6}*1728g, {2,6,3,6}*1728a, {2,6,3,6}*1728b, {2,6,3,12}*1728, {2,12,3,6}*1728
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29);;
s2 := ( 3,12)( 4,14)( 5,13)( 6,18)( 7,20)( 8,19)( 9,15)(10,17)(11,16)(22,23)
(24,27)(25,29)(26,28);;
s3 := ( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,25)(13,24)(14,26)(15,22)(16,21)(17,23)
(18,28)(19,27)(20,29);;
s4 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29);
s2 := Sym(29)!( 3,12)( 4,14)( 5,13)( 6,18)( 7,20)( 8,19)( 9,15)(10,17)(11,16)
(22,23)(24,27)(25,29)(26,28);
s3 := Sym(29)!( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,25)(13,24)(14,26)(15,22)(16,21)
(17,23)(18,28)(19,27)(20,29);
s4 := Sym(29)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29);
poly := sub<Sym(29)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >;

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