Polytope of Type {2,5,4}

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

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

Permutation Representation (Magma) :

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

to this polytope