Polytope of Type {10,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,8}*320
if this polytope has a name.
Group : SmallGroup(320,1426)
Rank : 4
Schlafli Type : {10,2,8}
Number of vertices, edges, etc : 10, 10, 8, 8
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,8,2} of size 640
   {10,2,8,4} of size 1280
   {10,2,8,4} of size 1280
   {10,2,8,6} of size 1920
   {10,2,8,3} of size 1920
Vertex Figure Of :
   {2,10,2,8} of size 640
   {4,10,2,8} of size 1280
   {5,10,2,8} of size 1600
   {6,10,2,8} of size 1920
   {3,10,2,8} of size 1920
   {3,10,2,8} of size 1920
   {5,10,2,8} of size 1920
   {5,10,2,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,8}*160, {10,2,4}*160
   4-fold quotients : {5,2,4}*80, {10,2,2}*80
   5-fold quotients : {2,2,8}*64
   8-fold quotients : {5,2,2}*40
   10-fold quotients : {2,2,4}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,2,8}*640, {10,4,8}*640a, {10,2,16}*640
   3-fold covers : {10,2,24}*960, {10,6,8}*960, {30,2,8}*960
   4-fold covers : {10,4,8}*1280a, {10,8,8}*1280a, {10,8,8}*1280b, {40,2,8}*1280, {20,4,8}*1280a, {10,4,16}*1280a, {10,4,16}*1280b, {20,2,16}*1280, {10,2,32}*1280
   5-fold covers : {50,2,8}*1600, {10,2,40}*1600, {10,10,8}*1600a, {10,10,8}*1600c
   6-fold covers : {30,4,8}*1920a, {10,12,8}*1920a, {10,4,24}*1920a, {60,2,8}*1920, {20,6,8}*1920, {20,2,24}*1920, {30,2,16}*1920, {10,6,16}*1920, {10,2,48}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope