Polytope of Type {10,2,2,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,2,2,2}*320
if this polytope has a name.
Group : SmallGroup(320,1639)
Rank : 6
Schlafli Type : {10,2,2,2,2}
Number of vertices, edges, etc : 10, 10, 2, 2, 2, 2
Order of s0s1s2s3s4s5 : 10
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,2,2,2,2} of size 640
   {10,2,2,2,2,3} of size 960
   {10,2,2,2,2,4} of size 1280
   {10,2,2,2,2,5} of size 1600
   {10,2,2,2,2,6} of size 1920
Vertex Figure Of :
   {2,10,2,2,2,2} of size 640
   {4,10,2,2,2,2} of size 1280
   {5,10,2,2,2,2} of size 1600
   {6,10,2,2,2,2} of size 1920
   {3,10,2,2,2,2} of size 1920
   {3,10,2,2,2,2} of size 1920
   {5,10,2,2,2,2} of size 1920
   {5,10,2,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,2,2,2}*160
   5-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,2,2,2,2}*640, {10,2,2,2,4}*640, {10,2,2,4,2}*640, {10,2,4,2,2}*640, {10,4,2,2,2}*640
   3-fold covers : {10,2,2,2,6}*960, {10,2,2,6,2}*960, {10,2,6,2,2}*960, {10,6,2,2,2}*960, {30,2,2,2,2}*960
   4-fold covers : {10,2,2,4,4}*1280, {10,2,4,4,2}*1280, {10,4,4,2,2}*1280, {20,4,2,2,2}*1280, {10,2,4,2,4}*1280, {10,4,2,2,4}*1280, {10,4,2,4,2}*1280, {20,2,2,2,4}*1280, {20,2,2,4,2}*1280, {20,2,4,2,2}*1280, {10,2,2,2,8}*1280, {10,2,2,8,2}*1280, {10,2,8,2,2}*1280, {10,8,2,2,2}*1280, {40,2,2,2,2}*1280
   5-fold covers : {50,2,2,2,2}*1600, {10,2,2,2,10}*1600, {10,2,2,10,2}*1600, {10,2,10,2,2}*1600, {10,10,2,2,2}*1600a, {10,10,2,2,2}*1600c
   6-fold covers : {30,2,2,2,4}*1920, {30,2,2,4,2}*1920, {30,2,4,2,2}*1920, {30,4,2,2,2}*1920a, {60,2,2,2,2}*1920, {10,2,2,4,6}*1920a, {10,2,2,6,4}*1920a, {10,2,4,2,6}*1920, {10,2,4,6,2}*1920a, {10,2,6,2,4}*1920, {10,2,6,4,2}*1920a, {10,4,2,2,6}*1920, {10,4,2,6,2}*1920, {10,4,6,2,2}*1920, {10,6,2,2,4}*1920, {10,6,2,4,2}*1920, {10,6,4,2,2}*1920a, {10,2,2,2,12}*1920, {10,2,2,12,2}*1920, {10,2,12,2,2}*1920, {10,12,2,2,2}*1920, {20,2,2,2,6}*1920, {20,2,2,6,2}*1920, {20,2,6,2,2}*1920, {20,6,2,2,2}*1920a
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,12);;
s3 := (13,14);;
s4 := (15,16);;
s5 := (17,18);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, 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)!(11,12);
s3 := Sym(18)!(13,14);
s4 := Sym(18)!(15,16);
s5 := Sym(18)!(17,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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