Polytope of Type {12,3,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3,6,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {12,3,6,2}
Number of vertices, edges, etc : 24, 36, 18, 6, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,3,6,2}*576, {12,3,2,2}*576
   4-fold quotients : {6,3,6,2}*432
   6-fold quotients : {4,3,6,2}*288
   9-fold quotients : {4,3,2,2}*192
   12-fold quotients : {2,3,6,2}*144, {6,3,2,2}*144
   18-fold quotients : {4,3,2,2}*96
   36-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,15)(14,16)(17,23)(18,24)
(19,21)(20,22)(25,27)(26,28)(29,35)(30,36)(31,33)(32,34);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)(17,25)
(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36);;
s2 := ( 1,13)( 2,16)( 3,15)( 4,14)( 5,21)( 6,24)( 7,23)( 8,22)( 9,17)(10,20)
(11,19)(12,18)(26,28)(29,33)(30,36)(31,35)(32,34);;
s3 := (13,25)(14,26)(15,27)(16,28)(17,29)(18,30)(19,31)(20,32)(21,33)(22,34)
(23,35)(24,36);;
s4 := (37,38);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,15)(14,16)(17,23)
(18,24)(19,21)(20,22)(25,27)(26,28)(29,35)(30,36)(31,33)(32,34);
s1 := Sym(38)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)
(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36);
s2 := Sym(38)!( 1,13)( 2,16)( 3,15)( 4,14)( 5,21)( 6,24)( 7,23)( 8,22)( 9,17)
(10,20)(11,19)(12,18)(26,28)(29,33)(30,36)(31,35)(32,34);
s3 := Sym(38)!(13,25)(14,26)(15,27)(16,28)(17,29)(18,30)(19,31)(20,32)(21,33)
(22,34)(23,35)(24,36);
s4 := Sym(38)!(37,38);
poly := sub<Sym(38)|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, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

to this polytope