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Polytope of Type {40,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*960c
if this polytope has a name.
Group : SmallGroup(960,5762)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 80, 240, 12
Order of s0s1s2 : 15
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {40,6,2} of size 1920
Vertex Figure Of :
   {2,40,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {20,6}*240b
   5-fold quotients : {8,6}*192a
   20-fold quotients : {4,6}*48b
   40-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,12}*1920c, {40,12}*1920d, {40,6}*1920a
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,73)(18,74)
(19,75)(20,76)(21,80)(22,79)(23,78)(24,77)(25,65)(26,66)(27,67)(28,68)(29,72)
(30,71)(31,70)(32,69)(33,57)(34,58)(35,59)(36,60)(37,64)(38,63)(39,62)(40,61)
(41,49)(42,50)(43,51)(44,52)(45,56)(46,55)(47,54)(48,53);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)
(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(33,65)(34,66)(35,68)(36,67)(37,76)
(38,75)(39,73)(40,74)(41,71)(42,72)(43,70)(44,69)(45,78)(46,77)(47,79)(48,80)
(51,52)(53,60)(54,59)(55,57)(56,58)(61,62);;
s2 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 5, 7)(14,16)(17,25)(18,28)(19,27)(20,26)
(21,23)(30,32)(33,41)(34,44)(35,43)(36,42)(37,39)(46,48)(49,57)(50,60)(51,59)
(52,58)(53,55)(62,64)(65,73)(66,76)(67,75)(68,74)(69,71)(78,80);;
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*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,73)
(18,74)(19,75)(20,76)(21,80)(22,79)(23,78)(24,77)(25,65)(26,66)(27,67)(28,68)
(29,72)(30,71)(31,70)(32,69)(33,57)(34,58)(35,59)(36,60)(37,64)(38,63)(39,62)
(40,61)(41,49)(42,50)(43,51)(44,52)(45,56)(46,55)(47,54)(48,53);
s1 := Sym(80)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)
(10,24)(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(33,65)(34,66)(35,68)(36,67)
(37,76)(38,75)(39,73)(40,74)(41,71)(42,72)(43,70)(44,69)(45,78)(46,77)(47,79)
(48,80)(51,52)(53,60)(54,59)(55,57)(56,58)(61,62);
s2 := Sym(80)!( 1, 9)( 2,12)( 3,11)( 4,10)( 5, 7)(14,16)(17,25)(18,28)(19,27)
(20,26)(21,23)(30,32)(33,41)(34,44)(35,43)(36,42)(37,39)(46,48)(49,57)(50,60)
(51,59)(52,58)(53,55)(62,64)(65,73)(66,76)(67,75)(68,74)(69,71)(78,80);
poly := sub<Sym(80)|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*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0 >; 
 
References : None.
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