Polytope of Type {2,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,36}*288
if this polytope has a name.
Group : SmallGroup(288,354)
Rank : 4
Schlafli Type : {2,2,36}
Number of vertices, edges, etc : 2, 2, 36, 36
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,36,2} of size 576
   {2,2,36,4} of size 1152
   {2,2,36,4} of size 1152
   {2,2,36,4} of size 1152
   {2,2,36,6} of size 1728
   {2,2,36,6} of size 1728
   {2,2,36,6} of size 1728
Vertex Figure Of :
   {2,2,2,36} of size 576
   {3,2,2,36} of size 864
   {4,2,2,36} of size 1152
   {5,2,2,36} of size 1440
   {6,2,2,36} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,18}*144
   3-fold quotients : {2,2,12}*96
   4-fold quotients : {2,2,9}*72
   6-fold quotients : {2,2,6}*48
   9-fold quotients : {2,2,4}*32
   12-fold quotients : {2,2,3}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,36}*576a, {4,2,36}*576, {2,2,72}*576
   3-fold covers : {2,2,108}*864, {2,6,36}*864a, {2,6,36}*864b, {6,2,36}*864
   4-fold covers : {4,4,36}*1152, {2,8,36}*1152a, {2,4,72}*1152a, {2,8,36}*1152b, {2,4,72}*1152b, {2,4,36}*1152a, {8,2,36}*1152, {4,2,72}*1152, {2,2,144}*1152, {2,4,36}*1152b
   5-fold covers : {2,10,36}*1440, {10,2,36}*1440, {2,2,180}*1440
   6-fold covers : {2,4,108}*1728a, {4,2,108}*1728, {2,2,216}*1728, {12,2,36}*1728, {4,6,36}*1728a, {6,4,36}*1728, {2,6,72}*1728a, {2,6,72}*1728b, {6,2,72}*1728, {2,12,36}*1728a, {2,12,36}*1728b, {4,6,36}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope