Polytope of Type {2,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10}*400
if this polytope has a name.
Group : SmallGroup(400,211)
Rank : 4
Schlafli Type : {2,4,10}
Number of vertices, edges, etc : 2, 10, 50, 25
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,10,2} of size 800
Vertex Figure Of :
   {2,2,4,10} of size 800
   {3,2,4,10} of size 1200
   {4,2,4,10} of size 1600
   {5,2,4,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,10}*800, {2,4,10}*800
   3-fold covers : {6,4,10}*1200, {2,12,10}*1200
   4-fold covers : {8,4,10}*1600, {2,8,10}*1600, {4,4,10}*1600, {2,4,20}*1600
   5-fold covers : {2,4,10}*2000, {2,20,10}*2000a, {2,20,10}*2000b, {2,20,10}*2000c, {2,20,10}*2000d, {10,4,10}*2000b, {2,20,10}*2000e
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 9,12)(10,11);;
s2 := ( 3, 8)( 4,10)( 5,12)( 6, 9)( 7,11);;
s3 := ( 3, 4)( 5, 7)( 9,12)(10,11);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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