Polytope of Type {2,4,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,15}*240
if this polytope has a name.
Group : SmallGroup(240,197)
Rank : 4
Schlafli Type : {2,4,15}
Number of vertices, edges, etc : 2, 4, 30, 15
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,15,2} of size 480
   {2,4,15,4} of size 960
   {2,4,15,6} of size 1440
   {2,4,15,4} of size 1920
Vertex Figure Of :
   {2,2,4,15} of size 480
   {3,2,4,15} of size 720
   {4,2,4,15} of size 960
   {5,2,4,15} of size 1200
   {6,2,4,15} of size 1440
   {7,2,4,15} of size 1680
   {8,2,4,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,15}*480, {2,4,30}*480b, {2,4,30}*480c
   3-fold covers : {2,4,45}*720
   4-fold covers : {4,4,15}*960a, {2,4,60}*960b, {2,4,60}*960c, {4,4,15}*960b, {2,8,15}*960, {2,4,30}*960
   5-fold covers : {2,4,75}*1200
   6-fold covers : {2,4,45}*1440, {2,4,90}*1440b, {2,4,90}*1440c, {6,4,15}*1440, {2,12,15}*1440, {2,12,30}*1440d
   7-fold covers : {2,4,105}*1680
   8-fold covers : {4,4,15}*1920a, {4,4,15}*1920b, {4,4,30}*1920b, {2,4,30}*1920a, {4,4,30}*1920c, {2,8,15}*1920a, {2,8,30}*1920a, {4,8,15}*1920, {2,4,120}*1920c, {2,4,120}*1920d, {8,4,15}*1920, {2,4,60}*1920b, {4,4,30}*1920d, {2,4,30}*1920b, {2,4,60}*1920c, {2,8,30}*1920b, {2,8,30}*1920c
Permutation Representation (GAP) :

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

to this polytope