Polytope of Type {8,2,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,15}*480
if this polytope has a name.
Group : SmallGroup(480,875)
Rank : 4
Schlafli Type : {8,2,15}
Number of vertices, edges, etc : 8, 8, 15, 15
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,15,2} of size 960
   {8,2,15,4} of size 1920
Vertex Figure Of :
   {2,8,2,15} of size 960
   {4,8,2,15} of size 1920
   {4,8,2,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,15}*240
   3-fold quotients : {8,2,5}*160
   4-fold quotients : {2,2,15}*120
   5-fold quotients : {8,2,3}*96
   6-fold quotients : {4,2,5}*80
   10-fold quotients : {4,2,3}*48
   12-fold quotients : {2,2,5}*40
   20-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,2,15}*960, {8,2,30}*960
   3-fold covers : {8,2,45}*1440, {24,2,15}*1440, {8,6,15}*1440
   4-fold covers : {32,2,15}*1920, {8,4,30}*1920a, {8,2,60}*1920, {16,2,30}*1920, {8,4,15}*1920
Permutation Representation (GAP) :

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