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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {2,3,12,6}
Number of vertices, edges, etc : 2, 6, 36, 72, 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 : {2,3,4,6}*576, {2,3,12,2}*576
   4-fold quotients : {2,3,6,6}*432b
   9-fold quotients : {2,3,4,2}*192
   12-fold quotients : {2,3,2,6}*144, {2,3,6,2}*144
   18-fold quotients : {2,3,4,2}*96
   24-fold quotients : {2,3,2,3}*72
   36-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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