Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*320a
Also Known As : {20,8|2}. if this polytope has another name.
Group : SmallGroup(320,400)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 20, 80, 8
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,8,2} of size 640
   {20,8,4} of size 1280
   {20,8,4} of size 1280
   {20,8,6} of size 1920
   {20,8,3} of size 1920
Vertex Figure Of :
   {2,20,8} of size 640
   {4,20,8} of size 1280
   {6,20,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,4}*160, {10,8}*160
   4-fold quotients : {20,2}*80, {10,4}*80
   5-fold quotients : {4,8}*64a
   8-fold quotients : {10,2}*40
   10-fold quotients : {4,4}*32, {2,8}*32
   16-fold quotients : {5,2}*20
   20-fold quotients : {2,4}*16, {4,2}*16
   40-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,8}*640b, {20,8}*640a, {40,8}*640d, {20,16}*640a, {20,16}*640b
   3-fold covers : {20,24}*960a, {60,8}*960a
   4-fold covers : {40,8}*1280a, {20,8}*1280a, {40,8}*1280c, {20,16}*1280a, {20,16}*1280b, {80,8}*1280a, {80,8}*1280b, {40,16}*1280c, {80,8}*1280d, {40,16}*1280d, {40,16}*1280e, {80,8}*1280f, {40,16}*1280f, {20,32}*1280a, {20,32}*1280b
   5-fold covers : {100,8}*1600a, {20,40}*1600b, {20,40}*1600c
   6-fold covers : {60,8}*1920a, {20,24}*1920a, {120,8}*1920a, {120,8}*1920c, {40,24}*1920a, {40,24}*1920b, {60,16}*1920a, {20,48}*1920a, {60,16}*1920b, {20,48}*1920b
Permutation Representation (GAP) :

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