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Polytope of Type {2,36,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,36,2}*288
if this polytope has a name.
Group : SmallGroup(288,354)
Rank : 4
Schlafli Type : {2,36,2}
Number of vertices, edges, etc : 2, 36, 36, 2
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,36,2,2} of size 576
   {2,36,2,3} of size 864
   {2,36,2,4} of size 1152
   {2,36,2,5} of size 1440
   {2,36,2,6} of size 1728
Vertex Figure Of :
   {2,2,36,2} of size 576
   {3,2,36,2} of size 864
   {4,2,36,2} of size 1152
   {5,2,36,2} of size 1440
   {6,2,36,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,18,2}*144
   3-fold quotients : {2,12,2}*96
   4-fold quotients : {2,9,2}*72
   6-fold quotients : {2,6,2}*48
   9-fold quotients : {2,4,2}*32
   12-fold quotients : {2,3,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,36,4}*576a, {4,36,2}*576a, {2,72,2}*576
   3-fold covers : {2,108,2}*864, {2,36,6}*864a, {2,36,6}*864b, {6,36,2}*864a, {6,36,2}*864b
   4-fold covers : {4,36,4}*1152a, {2,36,8}*1152a, {8,36,2}*1152a, {2,72,4}*1152a, {4,72,2}*1152a, {2,36,8}*1152b, {8,36,2}*1152b, {2,72,4}*1152b, {4,72,2}*1152b, {2,36,4}*1152a, {4,36,2}*1152a, {2,144,2}*1152, {2,36,4}*1152b, {4,36,2}*1152b
   5-fold covers : {2,36,10}*1440, {10,36,2}*1440, {2,180,2}*1440
   6-fold covers : {2,108,4}*1728a, {4,108,2}*1728a, {2,216,2}*1728, {4,36,6}*1728a, {4,36,6}*1728b, {6,36,4}*1728a, {6,36,4}*1728b, {2,72,6}*1728a, {2,72,6}*1728b, {6,72,2}*1728a, {6,72,2}*1728b, {2,36,12}*1728a, {2,36,12}*1728b, {12,36,2}*1728a, {12,36,2}*1728b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);;
s3 := (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*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!(1,2);
s1 := Sym(40)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);
s2 := Sym(40)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);
s3 := Sym(40)!(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*s1*s0*s1, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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