Polytope of Type {6,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1728d
if this polytope has a name.
Group : SmallGroup(1728,47847)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 8, 72, 72, 9
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   12-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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