Polytope of Type {5,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12}*240
if this polytope has a name.
Group : SmallGroup(240,136)
Rank : 4
Schlafli Type : {5,2,12}
Number of vertices, edges, etc : 5, 5, 12, 12
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,12,2} of size 480
   {5,2,12,4} of size 960
   {5,2,12,4} of size 960
   {5,2,12,4} of size 960
   {5,2,12,3} of size 960
   {5,2,12,6} of size 1440
   {5,2,12,6} of size 1440
   {5,2,12,6} of size 1440
   {5,2,12,3} of size 1440
   {5,2,12,6} of size 1440
   {5,2,12,8} of size 1920
   {5,2,12,8} of size 1920
   {5,2,12,4} of size 1920
   {5,2,12,4} of size 1920
   {5,2,12,4} of size 1920
   {5,2,12,6} of size 1920
   {5,2,12,6} of size 1920
Vertex Figure Of :
   {2,5,2,12} of size 480
   {3,5,2,12} of size 1440
   {5,5,2,12} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,6}*120
   3-fold quotients : {5,2,4}*80
   4-fold quotients : {5,2,3}*60
   6-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,24}*480, {10,2,12}*480
   3-fold covers : {5,2,36}*720, {15,2,12}*720
   4-fold covers : {5,2,48}*960, {20,2,12}*960, {10,4,12}*960, {10,2,24}*960
   5-fold covers : {25,2,12}*1200, {5,10,12}*1200, {5,2,60}*1200
   6-fold covers : {5,2,72}*1440, {10,2,36}*1440, {15,2,24}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {30,2,12}*1440
   7-fold covers : {5,2,84}*1680, {35,2,12}*1680
   8-fold covers : {5,2,96}*1920, {20,4,12}*1920, {10,8,12}*1920a, {10,4,24}*1920a, {10,8,12}*1920b, {10,4,24}*1920b, {10,4,12}*1920a, {40,2,12}*1920, {20,2,24}*1920, {10,2,48}*1920, {10,4,12}*1920b
Permutation Representation (GAP) :

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