Polytope of Type {12,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,2,5}*480
if this polytope has a name.
Group : SmallGroup(480,1087)
Rank : 5
Schlafli Type : {12,2,2,5}
Number of vertices, edges, etc : 12, 12, 2, 5, 5
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,2,5,2} of size 960
Vertex Figure Of :
   {2,12,2,2,5} of size 960
   {4,12,2,2,5} of size 1920
   {4,12,2,2,5} of size 1920
   {4,12,2,2,5} of size 1920
   {3,12,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,2,5}*240
   3-fold quotients : {4,2,2,5}*160
   4-fold quotients : {3,2,2,5}*120
   6-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2,5}*960a, {24,2,2,5}*960, {12,2,2,10}*960
   3-fold covers : {36,2,2,5}*1440, {12,6,2,5}*1440a, {12,6,2,5}*1440b, {12,2,2,15}*1440
   4-fold covers : {12,8,2,5}*1920a, {24,4,2,5}*1920a, {12,8,2,5}*1920b, {24,4,2,5}*1920b, {12,4,2,5}*1920a, {48,2,2,5}*1920, {12,4,2,10}*1920a, {12,2,4,10}*1920, {12,2,2,20}*1920, {24,2,2,10}*1920, {12,4,2,5}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (13,14);;
s3 := (16,17)(18,19);;
s4 := (15,16)(17,18);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(19)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(19)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(19)!(13,14);
s3 := Sym(19)!(16,17)(18,19);
s4 := Sym(19)!(15,16)(17,18);
poly := sub<Sym(19)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope