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Polytope of Type {8,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,5}*480
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 3
Schlafli Type : {8,5}
Number of vertices, edges, etc : 48, 120, 30
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,5,2} of size 960
Vertex Figure Of :
   {2,8,5} of size 960
   {4,8,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,5}*240
   4-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,10}*960c
   3-fold covers : {8,15}*1440
   4-fold covers : {8,10}*1920b, {8,20}*1920c, {8,20}*1920d
Permutation Representation (GAP) :
s0 := ( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)
(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);;
s1 := ( 3,15)( 4, 7)( 8,10)( 9,16)(11,19)(12,36)(13,26)(14,17)(18,24)(20,32)
(21,33)(22,34)(23,31)(25,35)(27,30)(28,29)(37,40)(38,39);;
s2 := ( 1,11)( 2,12)( 5,24)( 6,25)( 7,36)( 8,19)(13,39)(14,40)(15,35)(16,18)
(17,28)(20,22)(21,23)(26,27)(29,34)(30,31)(32,37)(33,38);;
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*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)
(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);
s1 := Sym(40)!( 3,15)( 4, 7)( 8,10)( 9,16)(11,19)(12,36)(13,26)(14,17)(18,24)
(20,32)(21,33)(22,34)(23,31)(25,35)(27,30)(28,29)(37,40)(38,39);
s2 := Sym(40)!( 1,11)( 2,12)( 5,24)( 6,25)( 7,36)( 8,19)(13,39)(14,40)(15,35)
(16,18)(17,28)(20,22)(21,23)(26,27)(29,34)(30,31)(32,37)(33,38);
poly := sub<Sym(40)|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*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
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