Polytope of Type {3,20,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope