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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46139)
Rank : 5
Schlafli Type : {2,2,4,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 54
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {2,2,4,6}*864
   3-fold quotients : {2,2,4,6}*576
   6-fold quotients : {2,2,4,6}*288
   27-fold quotients : {2,2,4,2}*64
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)
(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)
(47,56)(48,58)(49,57);;
s3 := ( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(17,18)(20,28)(21,27)
(22,26)(29,30)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(44,45)(47,55)
(48,54)(49,53)(56,57);;
s4 := ( 5,35)( 6,36)( 7,37)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,53)
(15,54)(16,55)(17,50)(18,51)(19,52)(20,56)(21,57)(22,58)(23,44)(24,45)(25,46)
(26,41)(27,42)(28,43)(29,47)(30,48)(31,49);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)
(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)
(46,54)(47,56)(48,58)(49,57);
s3 := Sym(58)!( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(17,18)(20,28)
(21,27)(22,26)(29,30)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(44,45)
(47,55)(48,54)(49,53)(56,57);
s4 := Sym(58)!( 5,35)( 6,36)( 7,37)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)
(14,53)(15,54)(16,55)(17,50)(18,51)(19,52)(20,56)(21,57)(22,58)(23,44)(24,45)
(25,46)(26,41)(27,42)(28,43)(29,47)(30,48)(31,49);
poly := sub<Sym(58)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3 >;

to this polytope