Polytope of Type {13,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,36}*1872
if this polytope has a name.
Group : SmallGroup(1872,188)
Rank : 4
Schlafli Type : {13,2,36}
Number of vertices, edges, etc : 13, 13, 36, 36
Order of s₀s₁s₂s₃ : 468
Order of s₀s₁s₂s₃s₂s₁ : 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 : {13,2,18}*936
   3-fold quotients : {13,2,12}*624
   4-fold quotients : {13,2,9}*468
   6-fold quotients : {13,2,6}*312
   9-fold quotients : {13,2,4}*208
   12-fold quotients : {13,2,3}*156
   18-fold quotients : {13,2,2}*104
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (15,16)(17,18)(20,23)(21,22)(24,25)(26,27)(28,31)(29,30)(32,33)(34,35)
(36,39)(37,38)(40,41)(42,43)(44,47)(45,46)(48,49);;
s3 := (14,20)(15,17)(16,26)(18,28)(19,22)(21,24)(23,34)(25,36)(27,30)(29,32)
(31,42)(33,44)(35,38)(37,40)(39,48)(41,45)(43,46)(47,49);;
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*s0*s1*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(49)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(49)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(49)!(15,16)(17,18)(20,23)(21,22)(24,25)(26,27)(28,31)(29,30)(32,33)
(34,35)(36,39)(37,38)(40,41)(42,43)(44,47)(45,46)(48,49);
s3 := Sym(49)!(14,20)(15,17)(16,26)(18,28)(19,22)(21,24)(23,34)(25,36)(27,30)
(29,32)(31,42)(33,44)(35,38)(37,40)(39,48)(41,45)(43,46)(47,49);
poly := sub<Sym(49)|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*s0*s1*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 >;

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