Polytope of Type {36,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,2,4}*576
if this polytope has a name.
Group : SmallGroup(576,1533)
Rank : 4
Schlafli Type : {36,2,4}
Number of vertices, edges, etc : 36, 36, 4, 4
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {36,2,4,2} of size 1152
   {36,2,4,3} of size 1728
Vertex Figure Of :
   {2,36,2,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {36,2,2}*288, {18,2,4}*288
   3-fold quotients : {12,2,4}*192
   4-fold quotients : {9,2,4}*144, {18,2,2}*144
   6-fold quotients : {12,2,2}*96, {6,2,4}*96
   8-fold quotients : {9,2,2}*72
   9-fold quotients : {4,2,4}*64
   12-fold quotients : {3,2,4}*48, {6,2,2}*48
   18-fold quotients : {2,2,4}*32, {4,2,2}*32
   24-fold quotients : {3,2,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {36,4,4}*1152, {36,2,8}*1152, {72,2,4}*1152
   3-fold covers : {108,2,4}*1728, {36,2,12}*1728, {36,6,4}*1728a, {36,6,4}*1728b
Permutation Representation (GAP) :

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