Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 240, 480, 40
Order of s₀s₁s₂ : 20
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 : {24,4}*960a, {24,4}*960b, {12,4}*960b
   4-fold quotients : {12,4}*480a, {12,4}*480b, {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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