Polytope of Type {20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 3
Schlafli Type : {20,4}
Number of vertices, edges, etc : 240, 480, 48
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,4}*960a, {20,4}*960b, {10,4}*960
   4-fold quotients : {10,4}*480a, {10,4}*480b, {10,4}*480c
   8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   16-fold quotients : {5,4}*120
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope