Polytope of Type {5,2,2,3,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,3,2,2}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 7
Schlafli Type : {5,2,2,3,2,2}
Number of vertices, edges, etc : 5, 5, 2, 3, 3, 2, 2
Order of s0s1s2s3s4s5s6 : 30
Order of s0s1s2s3s4s5s6s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,2,3,2,2,2} of size 960
   {5,2,2,3,2,2,3} of size 1440
   {5,2,2,3,2,2,4} of size 1920
Vertex Figure Of :
   {2,5,2,2,3,2,2} of size 960
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,2,3,2,4}*960, {5,2,2,6,2,2}*960, {10,2,2,3,2,2}*960
   3-fold covers : {5,2,2,9,2,2}*1440, {5,2,2,3,2,6}*1440, {5,2,2,3,6,2}*1440, {5,2,6,3,2,2}*1440, {15,2,2,3,2,2}*1440
   4-fold covers : {5,2,2,3,2,8}*1920, {5,2,2,6,2,4}*1920, {5,2,2,6,4,2}*1920a, {5,2,4,6,2,2}*1920a, {10,2,2,3,2,4}*1920, {10,4,2,3,2,2}*1920, {5,2,2,12,2,2}*1920, {20,2,2,3,2,2}*1920, {10,2,2,6,2,2}*1920, {5,2,2,3,4,2}*1920, {5,2,4,3,2,2}*1920
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10);;
s4 := (8,9);;
s5 := (11,12);;
s6 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s5*s6*s5*s6, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(2,3)(4,5);
s1 := Sym(14)!(1,2)(3,4);
s2 := Sym(14)!(6,7);
s3 := Sym(14)!( 9,10);
s4 := Sym(14)!(8,9);
s5 := Sym(14)!(11,12);
s6 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5,s6>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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