Polytope of Type {4,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6}*432
Also Known As : {{4,3}₃,{3,6}₆}. if this polytope has another name.
Group : SmallGroup(432,523)
Rank : 4
Schlafli Type : {4,3,6}
Number of vertices, edges, etc : 4, 18, 27, 18
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,6,2} of size 864
   {4,3,6,3} of size 1296
   {4,3,6,4} of size 1728
Vertex Figure Of :
   {2,4,3,6} of size 864
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,3,6}*144
   9-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,6}*864, {4,6,6}*864d, {4,6,6}*864f
   3-fold covers : {4,3,18}*1296, {4,3,6}*1296a, {4,9,6}*1296a, {4,9,6}*1296b, {4,9,6}*1296c, {4,9,6}*1296d
   4-fold covers : {4,12,6}*1728d, {4,12,6}*1728f, {8,3,6}*1728, {4,6,12}*1728e, {4,3,6}*1728, {4,6,6}*1728a, {4,3,12}*1728
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

References : None.
to this polytope