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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,15}*480
if this polytope has a name.
Group : SmallGroup(480,1199)
Rank : 5
Schlafli Type : {2,2,4,15}
Number of vertices, edges, etc : 2, 2, 4, 30, 15
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,15,2} of size 960
   {2,2,4,15,4} of size 1920
Vertex Figure Of :
   {2,2,2,4,15} of size 960
   {3,2,2,4,15} of size 1440
   {4,2,2,4,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,4,15}*960, {2,2,4,15}*960, {2,2,4,30}*960b, {2,2,4,30}*960c
   3-fold covers : {2,2,4,45}*1440, {6,2,4,15}*1440
   4-fold covers : {2,4,4,15}*1920a, {8,2,4,15}*1920, {2,2,4,60}*1920b, {2,2,4,60}*1920c, {2,4,4,15}*1920b, {4,2,4,15}*1920, {4,2,4,30}*1920b, {4,2,4,30}*1920c, {2,2,8,15}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 8)( 6,10)( 7,12)( 9,15)(11,19)(13,14)(16,20)(17,18)(21,24)(22,23);;
s3 := ( 6, 7)( 8,13)( 9,11)(10,16)(12,17)(15,21)(18,20)(19,22)(23,24);;
s4 := ( 5, 6)( 7, 9)( 8,10)(12,15)(13,18)(14,17)(16,23)(20,22)(21,24);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, 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(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!( 5, 8)( 6,10)( 7,12)( 9,15)(11,19)(13,14)(16,20)(17,18)(21,24)
(22,23);
s3 := Sym(24)!( 6, 7)( 8,13)( 9,11)(10,16)(12,17)(15,21)(18,20)(19,22)(23,24);
s4 := Sym(24)!( 5, 6)( 7, 9)( 8,10)(12,15)(13,18)(14,17)(16,23)(20,22)(21,24);
poly := sub<Sym(24)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
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 >;

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