Polytope of Type {16,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,40}*1280b
if this polytope has a name.
Group : SmallGroup(1280,82983)
Rank : 3
Schlafli Type : {16,40}
Number of vertices, edges, etc : 16, 320, 40
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {8,40}*640a
   4-fold quotients : {4,40}*320a, {8,20}*320b
   5-fold quotients : {16,8}*256b
   8-fold quotients : {4,20}*160, {2,40}*160
   10-fold quotients : {8,8}*128a
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {4,8}*64a, {8,4}*64b
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {2,8}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)
(11,56)(12,57)(13,58)(14,59)(15,60)(16,51)(17,52)(18,53)(19,54)(20,55)(21,76)
(22,77)(23,78)(24,79)(25,80)(26,71)(27,72)(28,73)(29,74)(30,75)(31,66)(32,67)
(33,68)(34,69)(35,70)(36,61)(37,62)(38,63)(39,64)(40,65);;
s1 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)(21,36)
(22,40)(23,39)(24,38)(25,37)(26,31)(27,35)(28,34)(29,33)(30,32)(41,61)(42,65)
(43,64)(44,63)(45,62)(46,66)(47,70)(48,69)(49,68)(50,67)(51,76)(52,80)(53,79)
(54,78)(55,77)(56,71)(57,75)(58,74)(59,73)(60,72);;
s2 := ( 1, 4)( 2, 3)( 6, 9)( 7, 8)(11,19)(12,18)(13,17)(14,16)(15,20)(21,34)
(22,33)(23,32)(24,31)(25,35)(26,39)(27,38)(28,37)(29,36)(30,40)(41,44)(42,43)
(46,49)(47,48)(51,59)(52,58)(53,57)(54,56)(55,60)(61,74)(62,73)(63,72)(64,71)
(65,75)(66,79)(67,78)(68,77)(69,76)(70,80);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)
(10,50)(11,56)(12,57)(13,58)(14,59)(15,60)(16,51)(17,52)(18,53)(19,54)(20,55)
(21,76)(22,77)(23,78)(24,79)(25,80)(26,71)(27,72)(28,73)(29,74)(30,75)(31,66)
(32,67)(33,68)(34,69)(35,70)(36,61)(37,62)(38,63)(39,64)(40,65);
s1 := Sym(80)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)
(21,36)(22,40)(23,39)(24,38)(25,37)(26,31)(27,35)(28,34)(29,33)(30,32)(41,61)
(42,65)(43,64)(44,63)(45,62)(46,66)(47,70)(48,69)(49,68)(50,67)(51,76)(52,80)
(53,79)(54,78)(55,77)(56,71)(57,75)(58,74)(59,73)(60,72);
s2 := Sym(80)!( 1, 4)( 2, 3)( 6, 9)( 7, 8)(11,19)(12,18)(13,17)(14,16)(15,20)
(21,34)(22,33)(23,32)(24,31)(25,35)(26,39)(27,38)(28,37)(29,36)(30,40)(41,44)
(42,43)(46,49)(47,48)(51,59)(52,58)(53,57)(54,56)(55,60)(61,74)(62,73)(63,72)
(64,71)(65,75)(66,79)(67,78)(68,77)(69,76)(70,80);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
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