Polytope of Type {2,15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,4}*240
if this polytope has a name.
Group : SmallGroup(240,197)
Rank : 4
Schlafli Type : {2,15,4}
Number of vertices, edges, etc : 2, 15, 30, 4
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,15,4,2} of size 480
   {2,15,4,4} of size 1920
Vertex Figure Of :
   {2,2,15,4} of size 480
   {3,2,15,4} of size 720
   {4,2,15,4} of size 960
   {5,2,15,4} of size 1200
   {6,2,15,4} of size 1440
   {7,2,15,4} of size 1680
   {8,2,15,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,15,4}*480, {2,30,4}*480b, {2,30,4}*480c
   3-fold covers : {2,45,4}*720, {6,15,4}*720
   4-fold covers : {2,60,4}*960b, {2,60,4}*960c, {4,30,4}*960b, {2,15,8}*960, {2,30,4}*960, {4,15,4}*960b
   5-fold covers : {2,75,4}*1200, {10,15,4}*1200
   6-fold covers : {2,45,4}*1440, {2,90,4}*1440b, {2,90,4}*1440c, {6,15,4}*1440b, {6,30,4}*1440d, {6,30,4}*1440e, {6,30,4}*1440f, {2,15,12}*1440, {2,30,12}*1440d
   7-fold covers : {2,105,4}*1680
   8-fold covers : {4,60,4}*1920b, {4,60,4}*1920c, {2,30,4}*1920a, {2,15,8}*1920a, {2,30,8}*1920a, {2,120,4}*1920c, {2,120,4}*1920d, {8,30,4}*1920b, {2,60,4}*1920b, {4,30,4}*1920a, {2,30,4}*1920b, {2,60,4}*1920c, {2,30,8}*1920b, {2,30,8}*1920c, {8,15,4}*1920, {4,15,4}*1920c, {4,30,4}*1920d, {4,30,4}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope