Polytope of Type {2,3,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12}*864
if this polytope has a name.
Group : SmallGroup(864,4000)
Rank : 4
Schlafli Type : {2,3,12}
Number of vertices, edges, etc : 2, 18, 108, 72
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,12,2} of size 1728
Vertex Figure Of :
   {2,2,3,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,12}*288
   4-fold quotients : {2,3,6}*216
   9-fold quotients : {2,3,4}*96
   12-fold quotients : {2,3,6}*72
   18-fold quotients : {2,3,4}*48
   36-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,24}*1728, {2,6,12}*1728a
Permutation Representation (GAP) :

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

to this polytope