Polytope of Type {2,15,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,2,3}*360
if this polytope has a name.
Group : SmallGroup(360,154)
Rank : 5
Schlafli Type : {2,15,2,3}
Number of vertices, edges, etc : 2, 15, 15, 3, 3
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,15,2,3,2} of size 720
   {2,15,2,3,3} of size 1440
   {2,15,2,3,4} of size 1440
Vertex Figure Of :
   {2,2,15,2,3} of size 720
   {3,2,15,2,3} of size 1080
   {4,2,15,2,3} of size 1440
   {5,2,15,2,3} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,5,2,3}*120
   5-fold quotients : {2,3,2,3}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,15,2,6}*720, {2,30,2,3}*720
   3-fold covers : {2,45,2,3}*1080, {2,15,2,9}*1080, {2,15,6,3}*1080, {6,15,2,3}*1080
   4-fold covers : {2,15,2,12}*1440, {2,60,2,3}*1440, {4,30,2,3}*1440a, {4,15,2,3}*1440, {2,30,2,6}*1440
   5-fold covers : {2,75,2,3}*1800, {10,15,2,3}*1800, {2,15,2,15}*1800
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s3 := (19,20);;
s4 := (18,19);;
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*s1*s0*s1, 
s0*s2*s0*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, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope