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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,3,2}*432b
if this polytope has a name.
Group : SmallGroup(432,759)
Rank : 5
Schlafli Type : {6,6,3,2}
Number of vertices, edges, etc : 6, 18, 9, 3, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,3,2,2} of size 864
   {6,6,3,2,3} of size 1296
   {6,6,3,2,4} of size 1728
Vertex Figure Of :
   {2,6,6,3,2} of size 864
   {3,6,6,3,2} of size 1296
   {4,6,6,3,2} of size 1728
   {3,6,6,3,2} of size 1728
   {4,6,6,3,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,3,2}*144, {6,2,3,2}*144
   6-fold quotients : {3,2,3,2}*72
   9-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,3,2}*864b, {6,6,6,2}*864c
   3-fold covers : {6,6,9,2}*1296b, {18,6,3,2}*1296b, {6,6,3,2}*1296c, {6,6,3,2}*1296d, {6,6,3,2}*1296e, {6,6,3,6}*1296b
   4-fold covers : {24,6,3,2}*1728b, {6,6,12,2}*1728c, {6,6,6,4}*1728e, {12,6,6,2}*1728e, {6,12,6,2}*1728g, {6,6,3,4}*1728b, {6,6,3,2}*1728, {6,12,3,2}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope