Polytope of Type {8,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,10}*320
if this polytope has a name.
Group : SmallGroup(320,1426)
Rank : 4
Schlafli Type : {8,2,10}
Number of vertices, edges, etc : 8, 8, 10, 10
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,10,2} of size 640
   {8,2,10,4} of size 1280
   {8,2,10,5} of size 1600
   {8,2,10,6} of size 1920
   {8,2,10,3} of size 1920
   {8,2,10,3} of size 1920
   {8,2,10,5} of size 1920
   {8,2,10,5} of size 1920
Vertex Figure Of :
   {2,8,2,10} of size 640
   {4,8,2,10} of size 1280
   {4,8,2,10} of size 1280
   {6,8,2,10} of size 1920
   {3,8,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,2,5}*160, {4,2,10}*160
   4-fold quotients : {4,2,5}*80, {2,2,10}*80
   5-fold quotients : {8,2,2}*64
   8-fold quotients : {2,2,5}*40
   10-fold quotients : {4,2,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,20}*640, {8,4,10}*640a, {16,2,10}*640
   3-fold covers : {24,2,10}*960, {8,6,10}*960, {8,2,30}*960
   4-fold covers : {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
   5-fold covers : {8,2,50}*1600, {40,2,10}*1600, {8,10,10}*1600a, {8,10,10}*1600c
   6-fold covers : {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
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope