Polytope of Type {4,20,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,240872)
Rank : 4
Schlafli Type : {4,20,3}
Number of vertices, edges, etc : 4, 160, 120, 12
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, {2,20,3}*960
   4-fold quotients : {4,10,3}*480, {2,10,3}*480
   8-fold quotients : {2,5,3}*240, {2,10,3}*240a, {2,10,3}*240b
   16-fold quotients : {2,5,3}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)(29,31)(30,32);;
s1 := ( 3, 4)( 7, 8)( 9,22)(10,21)(11,15)(12,16)(13,27)(14,28)(17,24)(18,23)
(25,26)(29,30)(33,34)(37,49)(38,50)(39,44)(40,43)(41,56)(42,55)(45,51)(46,52)
(47,48);;
s2 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,41)( 6,42)( 7,54)( 8,53)( 9,45)(10,46)
(11,51)(12,52)(13,34)(14,33)(15,56)(16,55)(17,38)(18,37)(19,49)(20,50)(21,48)
(22,47)(23,40)(24,39)(25,35)(26,36)(27,43)(28,44);;
s3 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,53)( 6,54)( 7,47)( 8,48)( 9,55)(10,56)
(11,44)(12,43)(13,50)(14,49)(15,39)(16,40)(17,52)(18,51)(19,36)(20,35)(21,41)
(22,42)(23,45)(24,46)(25,34)(26,33)(27,38)(28,37);;
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, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(56)!( 1, 3)( 2, 4)(29,31)(30,32);
s1 := Sym(56)!( 3, 4)( 7, 8)( 9,22)(10,21)(11,15)(12,16)(13,27)(14,28)(17,24)
(18,23)(25,26)(29,30)(33,34)(37,49)(38,50)(39,44)(40,43)(41,56)(42,55)(45,51)
(46,52)(47,48);
s2 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,41)( 6,42)( 7,54)( 8,53)( 9,45)
(10,46)(11,51)(12,52)(13,34)(14,33)(15,56)(16,55)(17,38)(18,37)(19,49)(20,50)
(21,48)(22,47)(23,40)(24,39)(25,35)(26,36)(27,43)(28,44);
s3 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,53)( 6,54)( 7,47)( 8,48)( 9,55)
(10,56)(11,44)(12,43)(13,50)(14,49)(15,39)(16,40)(17,52)(18,51)(19,36)(20,35)
(21,41)(22,42)(23,45)(24,46)(25,34)(26,33)(27,38)(28,37);
poly := sub<Sym(56)|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, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2 >;

References : None.
to this polytope