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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,20}*1600
if this polytope has a name.
Group : SmallGroup(1600,7723)
Rank : 5
Schlafli Type : {5,2,4,20}
Number of vertices, edges, etc : 5, 5, 4, 40, 20
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 : {5,2,2,20}*800, {5,2,4,10}*800
   4-fold quotients : {5,2,2,10}*400
   5-fold quotients : {5,2,4,4}*320
   8-fold quotients : {5,2,2,5}*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 := ( 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);;
s3 := ( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,31)(12,35)(13,34)(14,33)(15,32)
(16,36)(17,40)(18,39)(19,38)(20,37)(21,41)(22,45)(23,44)(24,43)(25,42)(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)(61,81)(62,85)(63,84)(64,83)(65,82);;
s4 := ( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)(26,37)(27,36)
(28,40)(29,39)(30,38)(31,42)(32,41)(33,45)(34,44)(35,43)(46,47)(48,50)(51,52)
(53,55)(56,57)(58,60)(61,62)(63,65)(66,77)(67,76)(68,80)(69,79)(70,78)(71,82)
(72,81)(73,85)(74,84)(75,83);;
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope