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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,10}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 5
Schlafli Type : {2,6,2,10}
Number of vertices, edges, etc : 2, 6, 6, 10, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,10,2} of size 960
   {2,6,2,10,4} of size 1920
Vertex Figure Of :
   {2,2,6,2,10} of size 960
   {3,2,6,2,10} of size 1440
   {4,2,6,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   3-fold quotients : {2,2,2,10}*160
   4-fold quotients : {2,3,2,5}*120
   5-fold quotients : {2,6,2,2}*96
   6-fold quotients : {2,2,2,5}*80
   10-fold quotients : {2,3,2,2}*48
   15-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,2,10}*960, {2,6,2,20}*960, {2,6,4,10}*960, {4,6,2,10}*960a
   3-fold covers : {2,18,2,10}*1440, {2,6,6,10}*1440a, {2,6,6,10}*1440c, {6,6,2,10}*1440a, {6,6,2,10}*1440b, {2,6,2,30}*1440
   4-fold covers : {2,12,4,10}*1920, {4,12,2,10}*1920a, {2,6,4,20}*1920, {4,6,4,10}*1920a, {4,6,2,20}*1920a, {2,12,2,20}*1920, {2,6,8,10}*1920, {8,6,2,10}*1920, {2,24,2,10}*1920, {2,6,2,40}*1920, {2,6,4,10}*1920, {4,6,2,10}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := (11,12)(13,14)(15,16)(17,18);;
s4 := ( 9,13)(10,11)(12,17)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!(1,2);
s1 := Sym(18)!(5,6)(7,8);
s2 := Sym(18)!(3,7)(4,5)(6,8);
s3 := Sym(18)!(11,12)(13,14)(15,16)(17,18);
s4 := Sym(18)!( 9,13)(10,11)(12,17)(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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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