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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,6,6}*1728e
if this polytope has a name.
Group : SmallGroup(1728,47915)
Rank : 6
Schlafli Type : {2,2,6,6,6}
Number of vertices, edges, etc : 2, 2, 6, 18, 18, 6
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   3-fold quotients : {2,2,2,6,6}*576c, {2,2,6,6,2}*576a
   6-fold quotients : {2,2,2,3,6}*288
   9-fold quotients : {2,2,2,6,2}*192, {2,2,6,2,2}*192
   18-fold quotients : {2,2,2,3,2}*96, {2,2,3,2,2}*96
   27-fold quotients : {2,2,2,2,2}*64
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)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58);;
s3 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,24)(15,23)(16,25)(17,30)(18,29)(19,31)
(20,27)(21,26)(22,28)(32,33)(35,39)(36,38)(37,40)(41,51)(42,50)(43,52)(44,57)
(45,56)(46,58)(47,54)(48,53)(49,55);;
s4 := ( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)(14,35)
(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)(25,55)
(26,50)(27,51)(28,52)(29,56)(30,57)(31,58);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40)(44,47)(45,48)(46,49)(53,56)(54,57)(55,58);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s4*s3*s2*s3*s4*s3, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4 ];;
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)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58);
s3 := Sym(58)!( 5, 6)( 8,12)( 9,11)(10,13)(14,24)(15,23)(16,25)(17,30)(18,29)
(19,31)(20,27)(21,26)(22,28)(32,33)(35,39)(36,38)(37,40)(41,51)(42,50)(43,52)
(44,57)(45,56)(46,58)(47,54)(48,53)(49,55);
s4 := Sym(58)!( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)
(14,35)(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)
(25,55)(26,50)(27,51)(28,52)(29,56)(30,57)(31,58);
s5 := Sym(58)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40)(44,47)(45,48)(46,49)(53,56)(54,57)(55,58);
poly := sub<Sym(58)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4 >;

to this polytope