Polytope of Type {5,2,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,15}*300
if this polytope has a name.
Group : SmallGroup(300,39)
Rank : 4
Schlafli Type : {5,2,15}
Number of vertices, edges, etc : 5, 5, 15, 15
Order of s₀s₁s₂s₃ : 15
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,15,2} of size 600
   {5,2,15,4} of size 1200
   {5,2,15,6} of size 1800
Vertex Figure Of :
   {2,5,2,15} of size 600
   {3,5,2,15} of size 1800
   {5,5,2,15} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,5}*100
   5-fold quotients : {5,2,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,30}*600, {10,2,15}*600
   3-fold covers : {5,2,45}*900, {15,2,15}*900
   4-fold covers : {20,2,15}*1200, {5,2,60}*1200, {10,2,30}*1200
   5-fold covers : {5,2,75}*1500, {25,2,15}*1500, {5,10,15}*1500
   6-fold covers : {5,2,90}*1800, {10,2,45}*1800, {10,6,15}*1800, {15,2,30}*1800, {30,2,15}*1800
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s3 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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