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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,3,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {2,12,3,6}
Number of vertices, edges, etc : 2, 24, 36, 18, 6
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 : {2,4,3,6}*576, {2,12,3,2}*576
   4-fold quotients : {2,6,3,6}*432
   6-fold quotients : {2,4,3,6}*288
   9-fold quotients : {2,4,3,2}*192
   12-fold quotients : {2,2,3,6}*144, {2,6,3,2}*144
   18-fold quotients : {2,4,3,2}*96
   36-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope