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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,5}*200
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 5
Schlafli Type : {5,2,2,5}
Number of vertices, edges, etc : 5, 5, 2, 5, 5
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,2,5,2} of size 400
   {5,2,2,5,3} of size 1200
   {5,2,2,5,5} of size 1200
   {5,2,2,5,10} of size 2000
Vertex Figure Of :
   {2,5,2,2,5} of size 400
   {3,5,2,2,5} of size 1200
   {5,5,2,2,5} of size 1200
   {10,5,2,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,2,10}*400, {10,2,2,5}*400
   3-fold covers : {5,2,2,15}*600, {15,2,2,5}*600
   4-fold covers : {5,2,2,20}*800, {20,2,2,5}*800, {5,2,4,10}*800, {10,4,2,5}*800, {10,2,2,10}*800
   5-fold covers : {5,2,2,25}*1000, {25,2,2,5}*1000, {5,2,10,5}*1000, {5,10,2,5}*1000
   6-fold covers : {5,2,6,10}*1200, {10,6,2,5}*1200, {5,2,2,30}*1200, {10,2,2,15}*1200, {15,2,2,10}*1200, {30,2,2,5}*1200
   7-fold covers : {5,2,2,35}*1400, {35,2,2,5}*1400
   8-fold covers : {5,2,4,20}*1600, {20,4,2,5}*1600, {5,2,2,40}*1600, {40,2,2,5}*1600, {5,2,8,10}*1600, {10,8,2,5}*1600, {10,2,2,20}*1600, {20,2,2,10}*1600, {10,2,4,10}*1600, {10,4,2,10}*1600
   9-fold covers : {5,2,2,45}*1800, {45,2,2,5}*1800, {5,2,6,15}*1800, {15,6,2,5}*1800, {15,2,2,15}*1800
   10-fold covers : {5,2,2,50}*2000, {10,2,2,25}*2000, {25,2,2,10}*2000, {50,2,2,5}*2000, {5,2,10,10}*2000a, {5,2,10,10}*2000b, {5,10,2,10}*2000, {10,2,10,5}*2000, {10,10,2,5}*2000a, {10,10,2,5}*2000c
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10)(11,12);;
s4 := ( 8, 9)(10,11);;
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, 
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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