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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6,2}*432b
if this polytope has a name.
Group : SmallGroup(432,759)
Rank : 5
Schlafli Type : {3,6,6,2}
Number of vertices, edges, etc : 3, 9, 18, 6, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,6,2,2} of size 864
   {3,6,6,2,3} of size 1296
   {3,6,6,2,4} of size 1728
Vertex Figure Of :
   {2,3,6,6,2} of size 864
   {4,3,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,6,2}*144, {3,6,2,2}*144
   6-fold quotients : {3,2,3,2}*72
   9-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,12,2}*864b, {3,6,6,4}*864d, {6,6,6,2}*864g
   3-fold covers : {3,6,18,2}*1296b, {9,6,6,2}*1296b, {3,6,6,2}*1296c, {3,6,6,2}*1296d, {3,6,6,2}*1296e, {3,6,6,6}*1296c, {3,6,6,6}*1296d
   4-fold covers : {3,6,24,2}*1728b, {3,6,6,8}*1728b, {3,6,12,4}*1728d, {12,6,6,2}*1728d, {6,6,12,2}*1728e, {6,12,6,2}*1728f, {6,6,6,4}*1728i, {3,6,6,4}*1728b, {3,6,6,2}*1728, {3,12,6,2}*1728b
Permutation Representation (GAP) :
s0 := ( 4, 7)( 5, 8)( 6, 9)(10,19)(11,20)(12,21)(13,25)(14,26)(15,27)(16,22)
(17,23)(18,24);;
s1 := ( 1,13)( 2,14)( 3,15)( 4,10)( 5,11)( 6,12)( 7,16)( 8,17)( 9,18)(19,22)
(20,23)(21,24);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)
(17,27)(18,26);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26);;
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, 
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!( 4, 7)( 5, 8)( 6, 9)(10,19)(11,20)(12,21)(13,25)(14,26)(15,27)
(16,22)(17,23)(18,24);
s1 := Sym(29)!( 1,13)( 2,14)( 3,15)( 4,10)( 5,11)( 6,12)( 7,16)( 8,17)( 9,18)
(19,22)(20,23)(21,24);
s2 := Sym(29)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)
(16,25)(17,27)(18,26);
s3 := Sym(29)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26);
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, s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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