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Polytope of Type {4,4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,5}*320
if this polytope has a name.
Group : SmallGroup(320,1260)
Rank : 5
Schlafli Type : {4,4,2,5}
Number of vertices, edges, etc : 4, 8, 4, 5, 5
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,5,2} of size 640
   {4,4,2,5,3} of size 1920
   {4,4,2,5,5} of size 1920
Vertex Figure Of :
   {2,4,4,2,5} of size 640
   {4,4,4,2,5} of size 1280
   {6,4,4,2,5} of size 1920
   {3,4,4,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
   4-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2,5}*640a, {8,4,2,5}*640a, {4,8,2,5}*640b, {8,4,2,5}*640b, {4,4,2,5}*640, {4,4,2,10}*640
   3-fold covers : {4,12,2,5}*960a, {12,4,2,5}*960a, {4,4,2,15}*960
   4-fold covers : {4,8,2,5}*1280a, {8,4,2,5}*1280a, {8,8,2,5}*1280a, {8,8,2,5}*1280b, {8,8,2,5}*1280c, {8,8,2,5}*1280d, {4,16,2,5}*1280a, {16,4,2,5}*1280a, {4,16,2,5}*1280b, {16,4,2,5}*1280b, {4,4,2,5}*1280, {4,8,2,5}*1280b, {8,4,2,5}*1280b, {4,4,4,10}*1280, {4,4,2,20}*1280, {4,8,2,10}*1280a, {8,4,2,10}*1280a, {4,8,2,10}*1280b, {8,4,2,10}*1280b, {4,4,2,10}*1280
   5-fold covers : {4,4,2,25}*1600, {4,20,2,5}*1600, {20,4,2,5}*1600, {4,4,10,5}*1600
   6-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,12,2,5}*1920a, {12,8,2,5}*1920a, {4,24,2,5}*1920a, {24,4,2,5}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,12,2,5}*1920b, {12,8,2,5}*1920b, {4,24,2,5}*1920b, {24,4,2,5}*1920b, {4,4,2,15}*1920, {4,12,2,5}*1920a, {12,4,2,5}*1920a, {4,4,2,30}*1920, {4,4,6,10}*1920, {4,12,2,10}*1920a, {12,4,2,10}*1920a
Permutation Representation (GAP) :
s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := (10,11)(12,13);;
s4 := ( 9,10)(11,12);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(2,3)(4,6);
s1 := Sym(13)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(13)!(2,4)(3,6);
s3 := Sym(13)!(10,11)(12,13);
s4 := Sym(13)!( 9,10)(11,12);
poly := sub<Sym(13)|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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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