Polytope of Type {8,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,5}*160
if this polytope has a name.
Group : SmallGroup(160,131)
Rank : 4
Schlafli Type : {8,2,5}
Number of vertices, edges, etc : 8, 8, 5, 5
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,5,2} of size 320
   {8,2,5,3} of size 960
   {8,2,5,5} of size 960
   {8,2,5,10} of size 1600
   {8,2,5,4} of size 1920
   {8,2,5,6} of size 1920
   {8,2,5,3} of size 1920
   {8,2,5,5} of size 1920
   {8,2,5,6} of size 1920
   {8,2,5,6} of size 1920
   {8,2,5,10} of size 1920
   {8,2,5,10} of size 1920
Vertex Figure Of :
   {2,8,2,5} of size 320
   {4,8,2,5} of size 640
   {4,8,2,5} of size 640
   {6,8,2,5} of size 960
   {3,8,2,5} of size 960
   {4,8,2,5} of size 1280
   {8,8,2,5} of size 1280
   {8,8,2,5} of size 1280
   {8,8,2,5} of size 1280
   {8,8,2,5} of size 1280
   {4,8,2,5} of size 1280
   {10,8,2,5} of size 1600
   {12,8,2,5} of size 1920
   {12,8,2,5} of size 1920
   {3,8,2,5} of size 1920
   {6,8,2,5} of size 1920
   {6,8,2,5} of size 1920
   {6,8,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,5}*80
   4-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,2,5}*320, {8,2,10}*320
   3-fold covers : {24,2,5}*480, {8,2,15}*480
   4-fold covers : {32,2,5}*640, {8,2,20}*640, {8,4,10}*640a, {16,2,10}*640
   5-fold covers : {8,2,25}*800, {40,2,5}*800, {8,10,5}*800
   6-fold covers : {48,2,5}*960, {16,2,15}*960, {24,2,10}*960, {8,6,10}*960, {8,2,30}*960
   7-fold covers : {56,2,5}*1120, {8,2,35}*1120
   8-fold covers : {64,2,5}*1280, {8,4,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,2,40}*1280, {8,4,20}*1280a, {16,4,10}*1280a, {16,4,10}*1280b, {16,2,20}*1280, {32,2,10}*1280
   9-fold covers : {72,2,5}*1440, {8,2,45}*1440, {24,2,15}*1440, {8,6,15}*1440
   10-fold covers : {16,2,25}*1600, {8,2,50}*1600, {80,2,5}*1600, {16,10,5}*1600, {40,2,10}*1600, {8,10,10}*1600a, {8,10,10}*1600c
   11-fold covers : {88,2,5}*1760, {8,2,55}*1760
   12-fold covers : {32,2,15}*1920, {96,2,5}*1920, {8,4,30}*1920a, {8,12,10}*1920a, {24,4,10}*1920a, {8,2,60}*1920, {8,6,20}*1920, {24,2,20}*1920, {16,2,30}*1920, {16,6,10}*1920, {48,2,10}*1920, {8,6,15}*1920, {8,4,15}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope