Polytope of Type {4,10,2,2,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,2,2,2,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 7
Schlafli Type : {4,10,2,2,2,3}
Number of vertices, edges, etc : 4, 20, 10, 2, 2, 3, 3
Order of s₀s₁s₂s₃s₄s₅s₆ : 60
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,2,2,2,3}*960
   4-fold quotients : {2,5,2,2,2,3}*480
   5-fold quotients : {4,2,2,2,2,3}*384
   10-fold quotients : {2,2,2,2,2,3}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 5)( 6,11)( 7,12)(13,17)(14,18);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,16)(12,15)(17,20)(18,19);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)(10,15)(12,17)(16,19);;
s3 := (21,22);;
s4 := (23,24);;
s5 := (26,27);;
s6 := (25,26);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s2*s0*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s5*s6*s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!( 2, 5)( 6,11)( 7,12)(13,17)(14,18);
s1 := Sym(27)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,16)(12,15)(17,20)
(18,19);
s2 := Sym(27)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)(10,15)(12,17)(16,19);
s3 := Sym(27)!(21,22);
s4 := Sym(27)!(23,24);
s5 := Sym(27)!(26,27);
s6 := Sym(27)!(25,26);
poly := sub<Sym(27)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6*s5*s6, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope