Polytope of Type {4,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240595)
Rank : 4
Schlafli Type : {4,10,6}
Number of vertices, edges, etc : 4, 80, 120, 24
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {4,10,3}*960, {4,10,6}*960b, {4,10,6}*960c, {2,10,6}*960c
   4-fold quotients : {4,10,3}*480, {2,5,6}*480b, {2,10,3}*480, {2,10,6}*480c, {2,10,6}*480d, {2,10,6}*480e, {2,10,6}*480f
   8-fold quotients : {2,5,3}*240, {2,5,6}*240b, {2,5,6}*240c, {2,10,3}*240a, {2,10,3}*240b
   16-fold quotients : {2,5,3}*120
   60-fold quotients : {4,2,2}*32
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16);;
s1 := ( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16)(18,21)(19,20);;
s2 := ( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(17,21)(18,20);;
s3 := ( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(18,20)(19,21);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope