Polytope of Type {5,2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,20,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,7723)
Rank : 5
Schlafli Type : {5,2,20,4}
Number of vertices, edges, etc : 5, 5, 20, 40, 4
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {5,2,20,2}*800, {5,2,10,4}*800
   4-fold quotients : {5,2,10,2}*400
   5-fold quotients : {5,2,4,4}*320
   8-fold quotients : {5,2,5,2}*200
   10-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
   20-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,36)(27,40)
(28,39)(29,38)(30,37)(31,41)(32,45)(33,44)(34,43)(35,42)(47,50)(48,49)(52,55)
(53,54)(57,60)(58,59)(62,65)(63,64)(66,76)(67,80)(68,79)(69,78)(70,77)(71,81)
(72,85)(73,84)(74,83)(75,82);;
s3 := ( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,32)(12,31)(13,35)(14,34)(15,33)
(16,37)(17,36)(18,40)(19,39)(20,38)(21,42)(22,41)(23,45)(24,44)(25,43)(46,67)
(47,66)(48,70)(49,69)(50,68)(51,72)(52,71)(53,75)(54,74)(55,73)(56,77)(57,76)
(58,80)(59,79)(60,78)(61,82)(62,81)(63,85)(64,84)(65,83);;
s4 := ( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)
(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,71)
(27,72)(28,73)(29,74)(30,75)(31,66)(32,67)(33,68)(34,69)(35,70)(36,81)(37,82)
(38,83)(39,84)(40,85)(41,76)(42,77)(43,78)(44,79)(45,80);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(85)!(2,3)(4,5);
s1 := Sym(85)!(1,2)(3,4);
s2 := Sym(85)!( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,36)
(27,40)(28,39)(29,38)(30,37)(31,41)(32,45)(33,44)(34,43)(35,42)(47,50)(48,49)
(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(66,76)(67,80)(68,79)(69,78)(70,77)
(71,81)(72,85)(73,84)(74,83)(75,82);
s3 := Sym(85)!( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,32)(12,31)(13,35)(14,34)
(15,33)(16,37)(17,36)(18,40)(19,39)(20,38)(21,42)(22,41)(23,45)(24,44)(25,43)
(46,67)(47,66)(48,70)(49,69)(50,68)(51,72)(52,71)(53,75)(54,74)(55,73)(56,77)
(57,76)(58,80)(59,79)(60,78)(61,82)(62,81)(63,85)(64,84)(65,83);
s4 := Sym(85)!( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)
(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)
(26,71)(27,72)(28,73)(29,74)(30,75)(31,66)(32,67)(33,68)(34,69)(35,70)(36,81)
(37,82)(38,83)(39,84)(40,85)(41,76)(42,77)(43,78)(44,79)(45,80);
poly := sub<Sym(85)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope