Polytope of Type {2,4,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,6}*1728d
if this polytope has a name.
Group : SmallGroup(1728,47870)
Rank : 5
Schlafli Type : {2,4,12,6}
Number of vertices, edges, etc : 2, 4, 36, 54, 9
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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