Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*864d
if this polytope has a name.
Group : SmallGroup(864,4000)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 18, 108, 36
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2} of size 1728
Vertex Figure Of :
   {2,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,12}*288d
   4-fold quotients : {2,6,6}*216
   9-fold quotients : {2,6,4}*96b
   18-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12}*1728b
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 := ( 5, 6)( 9,10)(13,14)(15,35)(16,36)(17,38)(18,37)(19,27)(20,28)(21,30)
(22,29)(23,31)(24,32)(25,34)(26,33);;
s3 := ( 3,18)( 4,17)( 5,16)( 6,15)( 7,26)( 8,25)( 9,24)(10,23)(11,22)(12,21)
(13,20)(14,19)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 5, 6)( 9,10)(13,14)(15,35)(16,36)(17,38)(18,37)(19,27)(20,28)
(21,30)(22,29)(23,31)(24,32)(25,34)(26,33);
s3 := Sym(38)!( 3,18)( 4,17)( 5,16)( 6,15)( 7,26)( 8,25)( 9,24)(10,23)(11,22)
(12,21)(13,20)(14,19)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35);
poly := sub<Sym(38)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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