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Polytope of Type {2,10,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,2,3,2}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 6
Schlafli Type : {2,10,2,3,2}
Number of vertices, edges, etc : 2, 10, 10, 3, 3, 2
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,2,3,2,2} of size 960
   {2,10,2,3,2,3} of size 1440
   {2,10,2,3,2,4} of size 1920
Vertex Figure Of :
   {2,2,10,2,3,2} of size 960
   {3,2,10,2,3,2} of size 1440
   {4,2,10,2,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,2,3,2}*240
   5-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,2,3,2}*960, {4,10,2,3,2}*960, {2,10,2,6,2}*960
   3-fold covers : {2,10,2,9,2}*1440, {2,10,2,3,6}*1440, {2,10,6,3,2}*1440, {6,10,2,3,2}*1440, {2,30,2,3,2}*1440
   4-fold covers : {4,20,2,3,2}*1920, {8,10,2,3,2}*1920, {2,40,2,3,2}*1920, {2,10,2,6,4}*1920a, {2,10,4,6,2}*1920, {4,10,2,6,2}*1920, {2,10,2,12,2}*1920, {2,20,2,6,2}*1920, {2,10,2,3,4}*1920, {2,10,4,3,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
s3 := (14,15);;
s4 := (13,14);;
s5 := (16,17);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*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, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(17)!(1,2);
s1 := Sym(17)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(17)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
s3 := Sym(17)!(14,15);
s4 := Sym(17)!(13,14);
s5 := Sym(17)!(16,17);
poly := sub<Sym(17)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*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, s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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