Polytope of Type {4,2,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,10,2}*320
if this polytope has a name.
Group : SmallGroup(320,1612)
Rank : 5
Schlafli Type : {4,2,10,2}
Number of vertices, edges, etc : 4, 4, 10, 10, 2
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,10,2,2} of size 640
   {4,2,10,2,3} of size 960
   {4,2,10,2,4} of size 1280
   {4,2,10,2,5} of size 1600
   {4,2,10,2,6} of size 1920
Vertex Figure Of :
   {2,4,2,10,2} of size 640
   {3,4,2,10,2} of size 960
   {4,4,2,10,2} of size 1280
   {6,4,2,10,2} of size 1920
   {3,4,2,10,2} of size 1920
   {6,4,2,10,2} of size 1920
   {6,4,2,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   4-fold quotients : {2,2,5,2}*80
   5-fold quotients : {4,2,2,2}*64
   10-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,20,2}*640, {4,4,10,2}*640, {4,2,10,4}*640, {8,2,10,2}*640
   3-fold covers : {12,2,10,2}*960, {4,2,10,6}*960, {4,6,10,2}*960a, {4,2,30,2}*960
   4-fold covers : {4,4,20,2}*1280, {4,4,10,4}*1280, {4,2,20,4}*1280, {4,8,10,2}*1280a, {8,4,10,2}*1280a, {4,8,10,2}*1280b, {8,4,10,2}*1280b, {4,4,10,2}*1280, {4,2,10,8}*1280, {8,2,10,4}*1280, {8,2,20,2}*1280, {4,2,40,2}*1280, {16,2,10,2}*1280
   5-fold covers : {4,2,50,2}*1600, {20,2,10,2}*1600, {4,2,10,10}*1600a, {4,2,10,10}*1600c, {4,10,10,2}*1600a, {4,10,10,2}*1600c
   6-fold covers : {4,4,30,2}*1920, {4,4,10,6}*1920, {4,12,10,2}*1920a, {12,4,10,2}*1920, {4,2,30,4}*1920a, {4,2,60,2}*1920, {4,6,10,4}*1920a, {4,2,10,12}*1920, {12,2,10,4}*1920, {4,2,20,6}*1920a, {4,6,20,2}*1920a, {12,2,20,2}*1920, {8,2,30,2}*1920, {8,2,10,6}*1920, {8,6,10,2}*1920, {24,2,10,2}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s4 := (15,16);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(16)!(2,3);
s1 := Sym(16)!(1,2)(3,4);
s2 := Sym(16)!( 7, 8)( 9,10)(11,12)(13,14);
s3 := Sym(16)!( 5, 9)( 6, 7)( 8,13)(10,11)(12,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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 >;

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