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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,4,2}*640
if this polytope has a name.
Group : SmallGroup(640,21507)
Rank : 6
Schlafli Type : {2,2,10,4,2}
Number of vertices, edges, etc : 2, 2, 10, 20, 4, 2
Order of s₀s₁s₂s₃s₄s₅ : 20
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,10,4,2,2} of size 1280
   {2,2,10,4,2,3} of size 1920
Vertex Figure Of :
   {2,2,2,10,4,2} of size 1280
   {3,2,2,10,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,10,2,2}*320
   4-fold quotients : {2,2,5,2,2}*160
   5-fold quotients : {2,2,2,4,2}*128
   10-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,10,4,4}*1280, {2,2,20,4,2}*1280, {4,2,10,4,2}*1280, {2,4,10,4,2}*1280, {2,2,10,8,2}*1280
   3-fold covers : {2,2,30,4,2}*1920a, {2,2,10,4,6}*1920, {2,6,10,4,2}*1920, {6,2,10,4,2}*1920, {2,2,10,12,2}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24);;
s3 := ( 5, 7)( 6,15)( 8,12)( 9,10)(11,21)(14,19)(16,17)(18,22)(20,23);;
s4 := ( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,19)(16,20)(21,23)(22,24);;
s5 := (25,26);;
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*s1*s0*s1, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(26)!(1,2);
s1 := Sym(26)!(3,4);
s2 := Sym(26)!( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24);
s3 := Sym(26)!( 5, 7)( 6,15)( 8,12)( 9,10)(11,21)(14,19)(16,17)(18,22)(20,23);
s4 := Sym(26)!( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,19)(16,20)(21,23)
(22,24);
s5 := Sym(26)!(25,26);
poly := sub<Sym(26)|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*s1*s0*s1, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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