Polytope of Type {2,10,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,2,6}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 5
Schlafli Type : {2,10,2,6}
Number of vertices, edges, etc : 2, 10, 10, 6, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,2,6,2} of size 960
   {2,10,2,6,3} of size 1440
   {2,10,2,6,4} of size 1920
   {2,10,2,6,3} of size 1920
   {2,10,2,6,4} of size 1920
   {2,10,2,6,4} of size 1920
Vertex Figure Of :
   {2,2,10,2,6} of size 960
   {3,2,10,2,6} of size 1440
   {4,2,10,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
   3-fold quotients : {2,10,2,2}*160
   4-fold quotients : {2,5,2,3}*120
   5-fold quotients : {2,2,2,6}*96
   6-fold quotients : {2,5,2,2}*80
   10-fold quotients : {2,2,2,3}*48
   15-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,2,12}*960, {2,20,2,6}*960, {2,10,4,6}*960, {4,10,2,6}*960
   3-fold covers : {2,10,2,18}*1440, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {6,10,2,6}*1440, {2,30,2,6}*1440
   4-fold covers : {2,10,4,12}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {4,10,4,6}*1920, {4,10,2,12}*1920, {2,20,2,12}*1920, {2,10,8,6}*1920, {8,10,2,6}*1920, {2,10,2,24}*1920, {2,40,2,6}*1920, {2,10,4,6}*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 := (15,16)(17,18);;
s4 := (13,17)(14,15)(16,18);;
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*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, s3*s4*s3*s4*s3*s4*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(18)!(1,2);
s1 := Sym(18)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(18)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
s3 := Sym(18)!(15,16)(17,18);
s4 := Sym(18)!(13,17)(14,15)(16,18);
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*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, 
s3*s4*s3*s4*s3*s4*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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