Polytope of Type {6,2,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,36}*1728
if this polytope has a name.
Group : SmallGroup(1728,30764)
Rank : 5
Schlafli Type : {6,2,2,36}
Number of vertices, edges, etc : 6, 6, 2, 36, 36
Order of s₀s₁s₂s₃s₄ : 36
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 : {3,2,2,36}*864, {6,2,2,18}*864
   3-fold quotients : {2,2,2,36}*576, {6,2,2,12}*576
   4-fold quotients : {3,2,2,18}*432, {6,2,2,9}*432
   6-fold quotients : {2,2,2,18}*288, {3,2,2,12}*288, {6,2,2,6}*288
   8-fold quotients : {3,2,2,9}*216
   9-fold quotients : {2,2,2,12}*192, {6,2,2,4}*192
   12-fold quotients : {2,2,2,9}*144, {3,2,2,6}*144, {6,2,2,3}*144
   18-fold quotients : {3,2,2,4}*96, {2,2,2,6}*96, {6,2,2,2}*96
   24-fold quotients : {3,2,2,3}*72
   27-fold quotients : {2,2,2,4}*64
   36-fold quotients : {2,2,2,3}*48, {3,2,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope