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Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*432b
if this polytope has a name.
Group : SmallGroup(432,741)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 54, 108, 36
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 864
   {6,4,3} of size 1296
   {6,4,4} of size 1728
Vertex Figure Of :
   {2,6,4} of size 864
   {3,6,4} of size 1296
   {4,6,4} of size 1728
   {4,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4}*144
   6-fold quotients : {6,4}*72
   9-fold quotients : {6,4}*48a
   18-fold quotients : {6,2}*24
   27-fold quotients : {2,4}*16
   36-fold quotients : {3,2}*12
   54-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4}*864d, {6,8}*864b
   3-fold covers : {18,4}*1296b, {6,4}*1296a, {6,12}*1296j, {6,12}*1296l, {6,12}*1296s, {6,12}*1296t
   4-fold covers : {24,4}*1728f, {24,4}*1728g, {6,16}*1728b, {12,8}*1728g, {12,8}*1728h, {12,4}*1728c, {6,4}*1728
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);;
s2 := (4,7)(5,8)(6,9);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(18)!( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);
s2 := Sym(18)!(4,7)(5,8)(6,9);
poly := sub<Sym(18)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
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