Polytope of Type {4,2,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,15}*240
if this polytope has a name.
Group : SmallGroup(240,179)
Rank : 4
Schlafli Type : {4,2,15}
Number of vertices, edges, etc : 4, 4, 15, 15
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,15,2} of size 480
   {4,2,15,4} of size 960
   {4,2,15,6} of size 1440
   {4,2,15,6} of size 1920
   {4,2,15,4} of size 1920
Vertex Figure Of :
   {2,4,2,15} of size 480
   {3,4,2,15} of size 720
   {4,4,2,15} of size 960
   {6,4,2,15} of size 1440
   {3,4,2,15} of size 1440
   {6,4,2,15} of size 1440
   {6,4,2,15} of size 1440
   {8,4,2,15} of size 1920
   {8,4,2,15} of size 1920
   {4,4,2,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,15}*120
   3-fold quotients : {4,2,5}*80
   5-fold quotients : {4,2,3}*48
   6-fold quotients : {2,2,5}*40
   10-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,15}*480, {4,2,30}*480
   3-fold covers : {4,2,45}*720, {12,2,15}*720, {4,6,15}*720
   4-fold covers : {16,2,15}*960, {4,2,60}*960, {4,4,30}*960, {8,2,30}*960, {4,4,15}*960b
   5-fold covers : {4,2,75}*1200, {20,2,15}*1200, {4,10,15}*1200
   6-fold covers : {8,2,45}*1440, {4,2,90}*1440, {24,2,15}*1440, {8,6,15}*1440, {12,2,30}*1440, {4,6,30}*1440b, {4,6,30}*1440c
   7-fold covers : {28,2,15}*1680, {4,2,105}*1680
   8-fold covers : {32,2,15}*1920, {4,4,60}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {4,4,30}*1920a, {8,2,60}*1920, {4,2,120}*1920, {16,2,30}*1920, {4,8,15}*1920, {8,4,15}*1920, {4,4,30}*1920d
Permutation Representation (GAP) :

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

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