Polytope of Type {3,2,13,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,13,2}*312
if this polytope has a name.
Group : SmallGroup(312,54)
Rank : 5
Schlafli Type : {3,2,13,2}
Number of vertices, edges, etc : 3, 3, 13, 13, 2
Order of s₀s₁s₂s₃s₄ : 78
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,13,2,2} of size 624
   {3,2,13,2,3} of size 936
   {3,2,13,2,4} of size 1248
   {3,2,13,2,5} of size 1560
   {3,2,13,2,6} of size 1872
Vertex Figure Of :
   {2,3,2,13,2} of size 624
   {3,3,2,13,2} of size 1248
   {4,3,2,13,2} of size 1248
   {6,3,2,13,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,26,2}*624, {6,2,13,2}*624
   3-fold covers : {9,2,13,2}*936, {3,2,39,2}*936
   4-fold covers : {12,2,13,2}*1248, {3,2,52,2}*1248, {3,2,26,4}*1248, {6,2,26,2}*1248
   5-fold covers : {15,2,13,2}*1560, {3,2,65,2}*1560
   6-fold covers : {9,2,26,2}*1872, {18,2,13,2}*1872, {3,2,26,6}*1872, {3,6,26,2}*1872, {3,2,78,2}*1872, {6,2,39,2}*1872
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s4 := (17,18);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!(2,3);
s1 := Sym(18)!(1,2);
s2 := Sym(18)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s3 := Sym(18)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s4 := Sym(18)!(17,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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 >;

to this polytope