Polytope of Type {4,3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47847)
Rank : 5
Schlafli Type : {4,3,6,4}
Number of vertices, edges, etc : 4, 6, 27, 36, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   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) :
   9-fold quotients : {4,3,2,4}*192
   18-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope