Polytope of Type {40,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,16}*1280b
if this polytope has a name.
Group : SmallGroup(1280,82983)
Rank : 3
Schlafli Type : {40,16}
Number of vertices, edges, etc : 40, 320, 16
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 : {40,8}*640a
   4-fold quotients : {40,4}*320a, {20,8}*320b
   5-fold quotients : {8,16}*256b
   8-fold quotients : {20,4}*160, {40,2}*160
   10-fold quotients : {8,8}*128c
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {8,4}*64a, {4,8}*64b
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {8,2}*32
   64-fold quotients : {5,2}*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 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)(21,31)
(22,35)(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44)
(47,50)(48,49)(51,56)(52,60)(53,59)(54,58)(55,57)(61,71)(62,75)(63,74)(64,73)
(65,72)(66,76)(67,80)(68,79)(69,78)(70,77);;
s1 := ( 1, 4)( 2, 3)( 6, 9)( 7, 8)(11,19)(12,18)(13,17)(14,16)(15,20)(21,39)
(22,38)(23,37)(24,36)(25,40)(26,34)(27,33)(28,32)(29,31)(30,35)(41,64)(42,63)
(43,62)(44,61)(45,65)(46,69)(47,68)(48,67)(49,66)(50,70)(51,79)(52,78)(53,77)
(54,76)(55,80)(56,74)(57,73)(58,72)(59,71)(60,75);;
s2 := ( 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);;
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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