Polytope of Type {4,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5,2}*320
if this polytope has a name.
Group : SmallGroup(320,1636)
Rank : 4
Schlafli Type : {4,5,2}
Number of vertices, edges, etc : 16, 40, 20, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,5,2,2} of size 640
   {4,5,2,3} of size 960
   {4,5,2,4} of size 1280
   {4,5,2,5} of size 1600
   {4,5,2,6} of size 1920
Vertex Figure Of :
   {2,4,5,2} of size 640
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,5,2}*640a, {8,5,2}*640b, {4,5,2}*640, {4,10,2}*640a, {4,10,2}*640b
   3-fold covers : {4,15,2}*960
   4-fold covers : {4,10,4}*1280b, {4,20,2}*1280b, {4,20,2}*1280c, {8,5,2}*1280a, {8,10,2}*1280a, {8,10,2}*1280b, {8,10,2}*1280c, {8,10,2}*1280d, {4,5,2}*1280, {4,10,2}*1280a, {4,20,2}*1280d, {4,20,2}*1280e, {8,5,2}*1280b, {4,10,2}*1280b
   5-fold covers : {4,25,2}*1600, {4,5,10}*1600
   6-fold covers : {8,15,2}*1920b, {8,15,2}*1920c, {4,10,6}*1920a, {12,10,2}*1920a, {4,15,2}*1920, {4,30,2}*1920c, {4,30,2}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope