Polytope of Type {6,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,36}*864
if this polytope has a name.
Group : SmallGroup(864,2437)
Rank : 4
Schlafli Type : {6,2,36}
Number of vertices, edges, etc : 6, 6, 36, 36
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,36,2} of size 1728
Vertex Figure Of :
   {2,6,2,36} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,36}*432, {6,2,18}*432
   3-fold quotients : {2,2,36}*288, {6,2,12}*288
   4-fold quotients : {3,2,18}*216, {6,2,9}*216
   6-fold quotients : {2,2,18}*144, {3,2,12}*144, {6,2,6}*144
   8-fold quotients : {3,2,9}*108
   9-fold quotients : {2,2,12}*96, {6,2,4}*96
   12-fold quotients : {2,2,9}*72, {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   24-fold quotients : {3,2,3}*36
   27-fold quotients : {2,2,4}*32
   36-fold quotients : {2,2,3}*24, {3,2,2}*24
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,36}*1728, {6,4,36}*1728, {6,2,72}*1728
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope