Polytope of Type {36,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,6,2}*864c
if this polytope has a name.
Group : SmallGroup(864,3998)
Rank : 4
Schlafli Type : {36,6,2}
Number of vertices, edges, etc : 36, 108, 6, 2
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {36,6,2,2} of size 1728
Vertex Figure Of :
   {2,36,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {12,6,2}*288d
   9-fold quotients : {4,6,2}*96b
   18-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {36,6,2}*1728
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,31)(14,32)(15,29)(16,30)
(17,27)(18,28)(19,25)(20,26)(21,35)(22,36)(23,33)(24,34);;
s1 := ( 1,13)( 2,15)( 3,14)( 4,16)( 5,21)( 6,23)( 7,22)( 8,24)( 9,17)(10,19)
(11,18)(12,20)(25,29)(26,31)(27,30)(28,32)(34,35);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36);;
s3 := (37,38);;
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*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,31)(14,32)(15,29)
(16,30)(17,27)(18,28)(19,25)(20,26)(21,35)(22,36)(23,33)(24,34);
s1 := Sym(38)!( 1,13)( 2,15)( 3,14)( 4,16)( 5,21)( 6,23)( 7,22)( 8,24)( 9,17)
(10,19)(11,18)(12,20)(25,29)(26,31)(27,30)(28,32)(34,35);
s2 := Sym(38)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36);
s3 := Sym(38)!(37,38);
poly := sub<Sym(38)|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*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

to this polytope