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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,2,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,7723)
Rank : 5
Schlafli Type : {4,20,2,5}
Number of vertices, edges, etc : 4, 40, 20, 5, 5
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 : {2,20,2,5}*800, {4,10,2,5}*800
   4-fold quotients : {2,10,2,5}*400
   5-fold quotients : {4,4,2,5}*320
   8-fold quotients : {2,5,2,5}*200
   10-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
   20-fold quotients : {2,2,2,5}*80
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)
(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,66)
(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)
(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75);;
s1 := ( 1,21)( 2,25)( 3,24)( 4,23)( 5,22)( 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)(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);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,32)(22,31)
(23,35)(24,34)(25,33)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45)(46,47)
(48,50)(51,52)(53,55)(56,57)(58,60)(61,72)(62,71)(63,75)(64,74)(65,73)(66,77)
(67,76)(68,80)(69,79)(70,78);;
s3 := (82,83)(84,85);;
s4 := (81,82)(83,84);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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(85)!( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 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)
(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)
(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75);
s1 := Sym(85)!( 1,21)( 2,25)( 3,24)( 4,23)( 5,22)( 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)
(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);
s2 := Sym(85)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,32)
(22,31)(23,35)(24,34)(25,33)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45)
(46,47)(48,50)(51,52)(53,55)(56,57)(58,60)(61,72)(62,71)(63,75)(64,74)(65,73)
(66,77)(67,76)(68,80)(69,79)(70,78);
s3 := Sym(85)!(82,83)(84,85);
s4 := Sym(85)!(81,82)(83,84);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope