Polytope of Type {5,2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,16}*320
if this polytope has a name.
Group : SmallGroup(320,537)
Rank : 4
Schlafli Type : {5,2,16}
Number of vertices, edges, etc : 5, 5, 16, 16
Order of s₀s₁s₂s₃ : 80
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,16,2} of size 640
   {5,2,16,4} of size 1280
   {5,2,16,4} of size 1280
   {5,2,16,6} of size 1920
Vertex Figure Of :
   {2,5,2,16} of size 640
   {3,5,2,16} of size 1920
   {5,5,2,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,8}*160
   4-fold quotients : {5,2,4}*80
   8-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,32}*640, {10,2,16}*640
   3-fold covers : {5,2,48}*960, {15,2,16}*960
   4-fold covers : {5,2,64}*1280, {10,4,16}*1280a, {20,2,16}*1280, {10,2,32}*1280
   5-fold covers : {25,2,16}*1600, {5,2,80}*1600, {5,10,16}*1600
   6-fold covers : {15,2,32}*1920, {5,2,96}*1920, {30,2,16}*1920, {10,6,16}*1920, {10,2,48}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s3 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!(2,3)(4,5);
s1 := Sym(21)!(1,2)(3,4);
s2 := Sym(21)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
s3 := Sym(21)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);
poly := sub<Sym(21)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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