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

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

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

Permutation Representation (Magma) :

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

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