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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,15}*240
if this polytope has a name.
Group : SmallGroup(240,207)
Rank : 5
Schlafli Type : {2,2,2,15}
Number of vertices, edges, etc : 2, 2, 2, 15, 15
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,15,2} of size 480
   {2,2,2,15,4} of size 960
   {2,2,2,15,6} of size 1440
   {2,2,2,15,6} of size 1920
   {2,2,2,15,4} of size 1920
Vertex Figure Of :
   {2,2,2,2,15} of size 480
   {3,2,2,2,15} of size 720
   {4,2,2,2,15} of size 960
   {5,2,2,2,15} of size 1200
   {6,2,2,2,15} of size 1440
   {7,2,2,2,15} of size 1680
   {8,2,2,2,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,5}*80
   5-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,15}*480, {4,2,2,15}*480, {2,2,2,30}*480
   3-fold covers : {2,2,2,45}*720, {2,2,6,15}*720, {2,6,2,15}*720, {6,2,2,15}*720
   4-fold covers : {4,4,2,15}*960, {2,8,2,15}*960, {8,2,2,15}*960, {2,2,2,60}*960, {2,2,4,30}*960a, {2,4,2,30}*960, {4,2,2,30}*960, {2,2,4,15}*960
   5-fold covers : {2,2,2,75}*1200, {2,2,10,15}*1200, {2,10,2,15}*1200, {10,2,2,15}*1200
   6-fold covers : {2,4,2,45}*1440, {4,2,2,45}*1440, {2,2,2,90}*1440, {2,12,2,15}*1440, {12,2,2,15}*1440, {4,2,6,15}*1440, {4,6,2,15}*1440a, {6,4,2,15}*1440a, {2,4,6,15}*1440, {2,2,6,30}*1440b, {2,2,6,30}*1440c, {2,6,2,30}*1440, {6,2,2,30}*1440
   7-fold covers : {2,14,2,15}*1680, {14,2,2,15}*1680, {2,2,2,105}*1680
   8-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {4,4,2,15}*1920, {2,16,2,15}*1920, {16,2,2,15}*1920, {2,4,4,30}*1920, {4,4,2,30}*1920, {2,2,4,60}*1920a, {4,2,4,30}*1920a, {2,4,2,60}*1920, {4,2,2,60}*1920, {2,2,8,30}*1920, {2,8,2,30}*1920, {8,2,2,30}*1920, {2,2,2,120}*1920, {2,4,4,15}*1920b, {4,2,4,15}*1920, {2,2,8,15}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope