Polytope of Type {12,2,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,15}*720
if this polytope has a name.
Group : SmallGroup(720,672)
Rank : 4
Schlafli Type : {12,2,15}
Number of vertices, edges, etc : 12, 12, 15, 15
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,15,2} of size 1440
Vertex Figure Of :
   {2,12,2,15} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,15}*360
   3-fold quotients : {12,2,5}*240, {4,2,15}*240
   4-fold quotients : {3,2,15}*180
   5-fold quotients : {12,2,3}*144
   6-fold quotients : {6,2,5}*120, {2,2,15}*120
   9-fold quotients : {4,2,5}*80
   10-fold quotients : {6,2,3}*72
   12-fold quotients : {3,2,5}*60
   15-fold quotients : {4,2,3}*48
   18-fold quotients : {2,2,5}*40
   20-fold quotients : {3,2,3}*36
   30-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,2,15}*1440, {12,2,30}*1440
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 := (14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := (13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
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*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(27)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(27)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(27)!(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s3 := Sym(27)!(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
poly := sub<Sym(27)|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*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 >;

to this polytope