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Polytope of Type {3,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,9}*432
if this polytope has a name.
Group : SmallGroup(432,522)
Rank : 5
Schlafli Type : {3,2,4,9}
Number of vertices, edges, etc : 3, 3, 4, 18, 9
Order of s0s1s2s3s4 : 9
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,9,2} of size 864
   {3,2,4,9,4} of size 1728
Vertex Figure Of :
   {2,3,2,4,9} of size 864
   {3,3,2,4,9} of size 1728
   {4,3,2,4,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,9}*864, {3,2,4,18}*864b, {3,2,4,18}*864c, {6,2,4,9}*864
   3-fold covers : {3,2,4,27}*1296, {9,2,4,9}*1296
   4-fold covers : {3,2,4,36}*1728b, {3,2,4,36}*1728c, {12,2,4,9}*1728, {3,2,8,9}*1728, {3,2,4,18}*1728, {6,2,4,9}*1728, {6,2,4,18}*1728b, {6,2,4,18}*1728c
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)
(30,37)(32,38);;
s3 := ( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)
(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);;
s4 := ( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)
(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(39)!(2,3);
s1 := Sym(39)!(1,2);
s2 := Sym(39)!( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)
(28,36)(30,37)(32,38);
s3 := Sym(39)!( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)
(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);
s4 := Sym(39)!( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)
(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);
poly := sub<Sym(39)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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