Polytope of Type {18,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,2,2}*864a
if this polytope has a name.
Group : SmallGroup(864,4032)
Rank : 5
Schlafli Type : {18,6,2,2}
Number of vertices, edges, etc : 18, 54, 6, 2, 2
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {18,6,2,2,2} of size 1728
Vertex Figure Of :
   {2,18,6,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {18,2,2,2}*288, {6,6,2,2}*288a
   6-fold quotients : {9,2,2,2}*144
   9-fold quotients : {2,6,2,2}*96, {6,2,2,2}*96
   18-fold quotients : {2,3,2,2}*48, {3,2,2,2}*48
   27-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {18,12,2,2}*1728a, {36,6,2,2}*1728a, {18,6,2,4}*1728a, {18,6,4,2}*1728a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope