Polytope of Type {2,8,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2,5}*320
if this polytope has a name.
Group : SmallGroup(320,1426)
Rank : 5
Schlafli Type : {2,8,2,5}
Number of vertices, edges, etc : 2, 8, 8, 5, 5
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,2,5,2} of size 640
   {2,8,2,5,3} of size 1920
   {2,8,2,5,5} of size 1920
Vertex Figure Of :
   {2,2,8,2,5} of size 640
   {3,2,8,2,5} of size 960
   {4,2,8,2,5} of size 1280
   {5,2,8,2,5} of size 1600
   {6,2,8,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,5}*160
   4-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2,5}*640a, {2,16,2,5}*640, {2,8,2,10}*640
   3-fold covers : {2,24,2,5}*960, {6,8,2,5}*960, {2,8,2,15}*960
   4-fold covers : {4,8,2,5}*1280a, {8,8,2,5}*1280a, {8,8,2,5}*1280b, {4,16,2,5}*1280a, {4,16,2,5}*1280b, {2,32,2,5}*1280, {2,8,4,10}*1280a, {4,8,2,10}*1280a, {2,8,2,20}*1280, {2,16,2,10}*1280
   5-fold covers : {2,8,2,25}*1600, {2,40,2,5}*1600, {10,8,2,5}*1600, {2,8,10,5}*1600
   6-fold covers : {4,8,2,15}*1920a, {12,8,2,5}*1920a, {4,24,2,5}*1920a, {2,16,2,15}*1920, {6,16,2,5}*1920, {2,48,2,5}*1920, {2,8,2,30}*1920, {2,8,6,10}*1920, {6,8,2,10}*1920, {2,24,2,10}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (12,13)(14,15);;
s4 := (11,12)(13,14);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(1,2);
s1 := Sym(15)!(4,5)(6,7)(8,9);
s2 := Sym(15)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(15)!(12,13)(14,15);
s4 := Sym(15)!(11,12)(13,14);
poly := sub<Sym(15)|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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope