Polytope of Type {16,2,5}

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

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

Permutation Representation (Magma) :

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

to this polytope