Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 40, 480, 160
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,24}*960c, {6,24}*960d, {6,12}*960b
   4-fold quotients : {6,12}*480a, {6,12}*480b, {6,6}*480
   8-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   16-fold quotients : {6,6}*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)( 3,35)( 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);;
s2 := ( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)(10,36)
(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)
(22,48)(23,49)(24,50)(25,51)(26,52);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 3,35)( 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);
s2 := Sym(52)!( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)
(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)
(21,47)(22,48)(23,49)(24,50)(25,51)(26,52);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope