Polytope of Type {5,2,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,6}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 5
Schlafli Type : {5,2,2,6}
Number of vertices, edges, etc : 5, 5, 2, 6, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,2,6,2} of size 480
   {5,2,2,6,3} of size 720
   {5,2,2,6,4} of size 960
   {5,2,2,6,3} of size 960
   {5,2,2,6,4} of size 960
   {5,2,2,6,4} of size 960
   {5,2,2,6,4} of size 1440
   {5,2,2,6,6} of size 1440
   {5,2,2,6,6} of size 1440
   {5,2,2,6,6} of size 1440
   {5,2,2,6,8} of size 1920
   {5,2,2,6,4} of size 1920
   {5,2,2,6,6} of size 1920
Vertex Figure Of :
   {2,5,2,2,6} of size 480
   {3,5,2,2,6} of size 1440
   {5,5,2,2,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,2,3}*120
   3-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,2,12}*480, {5,2,4,6}*480a, {10,2,2,6}*480
   3-fold covers : {5,2,2,18}*720, {5,2,6,6}*720a, {5,2,6,6}*720b, {15,2,2,6}*720
   4-fold covers : {5,2,4,12}*960a, {5,2,2,24}*960, {5,2,8,6}*960, {10,2,2,12}*960, {20,2,2,6}*960, {10,2,4,6}*960a, {10,4,2,6}*960, {5,2,4,6}*960
   5-fold covers : {25,2,2,6}*1200, {5,2,10,6}*1200, {5,10,2,6}*1200, {5,2,2,30}*1200
   6-fold covers : {5,2,2,36}*1440, {5,2,4,18}*1440a, {10,2,2,18}*1440, {5,2,6,12}*1440a, {5,2,6,12}*1440b, {5,2,12,6}*1440a, {5,2,12,6}*1440c, {15,2,2,12}*1440, {15,2,4,6}*1440a, {10,2,6,6}*1440a, {10,2,6,6}*1440b, {10,6,2,6}*1440, {30,2,2,6}*1440
   7-fold covers : {5,2,14,6}*1680, {5,2,2,42}*1680, {35,2,2,6}*1680
   8-fold covers : {5,2,8,12}*1920a, {5,2,4,24}*1920a, {5,2,8,12}*1920b, {5,2,4,24}*1920b, {5,2,4,12}*1920a, {5,2,16,6}*1920, {5,2,2,48}*1920, {10,4,4,6}*1920, {10,2,4,12}*1920a, {20,4,2,6}*1920, {10,4,2,12}*1920, {20,2,4,6}*1920a, {20,2,2,12}*1920, {10,2,8,6}*1920, {10,8,2,6}*1920, {10,2,2,24}*1920, {40,2,2,6}*1920, {5,2,4,12}*1920b, {5,2,4,6}*1920b, {5,2,4,12}*1920c, {5,2,8,6}*1920b, {5,2,8,6}*1920c, {10,2,4,6}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := (10,11)(12,13);;
s4 := ( 8,12)( 9,10)(11,13);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope