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

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

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

Permutation Representation (Magma) :

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

to this polytope