Polytope of Type {6,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,3}*864b
if this polytope has a name.
Group : SmallGroup(864,4673)
Rank : 4
Schlafli Type : {6,12,3}
Number of vertices, edges, etc : 6, 72, 36, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,3,2} of size 1728
Vertex Figure Of :
   {2,6,12,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4,3}*288, {2,12,3}*288
   4-fold quotients : {6,6,3}*216b
   9-fold quotients : {2,4,3}*96
   12-fold quotients : {2,6,3}*72, {6,2,3}*72
   18-fold quotients : {2,4,3}*48
   24-fold quotients : {3,2,3}*36
   36-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,24,3}*1728b, {12,12,3}*1728b, {6,12,6}*1728f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope