Polytope of Type {3,2,4,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,15}*720
if this polytope has a name.
Group : SmallGroup(720,793)
Rank : 5
Schlafli Type : {3,2,4,15}
Number of vertices, edges, etc : 3, 3, 4, 30, 15
Order of s₀s₁s₂s₃s₄ : 15
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,15,2} of size 1440
Vertex Figure Of :
   {2,3,2,4,15} of size 1440
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,15}*1440, {3,2,4,30}*1440b, {3,2,4,30}*1440c, {6,2,4,15}*1440
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 7)( 5, 9)( 6,11)( 8,14)(10,18)(12,13)(15,19)(16,17)(20,23)(21,22);;
s3 := ( 5, 6)( 7,12)( 8,10)( 9,15)(11,16)(14,20)(17,19)(18,21)(22,23);;
s4 := ( 4, 5)( 6, 8)( 7, 9)(11,14)(12,17)(13,16)(15,22)(19,21)(20,23);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope