Polytope of Type {3,6,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,3,4}*432
if this polytope has a name.
Group : SmallGroup(432,523)
Rank : 5
Schlafli Type : {3,6,3,4}
Number of vertices, edges, etc : 3, 9, 9, 6, 4
Order of s₀s₁s₂s₃s₄ : 3
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,3,4,2} of size 864
Vertex Figure Of :
   {2,3,6,3,4} of size 864
   {4,3,6,3,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,3,4}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,3,4}*864, {3,6,6,4}*864b, {3,6,6,4}*864c, {6,6,3,4}*864a
   3-fold covers : {9,6,3,4}*1296, {3,6,3,4}*1296a, {3,6,9,4}*1296, {3,6,3,4}*1296b
   4-fold covers : {3,6,12,4}*1728b, {3,6,12,4}*1728c, {12,6,3,4}*1728a, {3,6,3,8}*1728, {3,6,6,4}*1728a, {6,6,3,4}*1728a, {6,6,6,4}*1728b, {6,6,6,4}*1728c
Permutation Representation (GAP) :

s0 := ( 5, 9)( 6,10)( 7,11)( 8,12)(13,25)(14,26)(15,27)(16,28)(17,33)(18,34)
(19,35)(20,36)(21,29)(22,30)(23,31)(24,32);;
s1 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)(10,18)
(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,33)(26,34)(27,36)(28,35)(31,32);;
s3 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);;
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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!( 5, 9)( 6,10)( 7,11)( 8,12)(13,25)(14,26)(15,27)(16,28)(17,33)
(18,34)(19,35)(20,36)(21,29)(22,30)(23,31)(24,32);
s1 := Sym(36)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)
(10,18)(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);
s2 := Sym(36)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,17)(14,18)(15,20)(16,19)
(23,24)(25,33)(26,34)(27,36)(28,35)(31,32);
s3 := Sym(36)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);
s4 := Sym(36)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);
poly := sub<Sym(36)|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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

References : None.
to this polytope