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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,20,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,364865)
Rank : 5
Schlafli Type : {4,2,20,4}
Number of vertices, edges, etc : 4, 4, 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 : {2,2,20,4}*640, {4,2,20,2}*640, {4,2,10,4}*640
   4-fold quotients : {2,2,20,2}*320, {2,2,10,4}*320, {4,2,10,2}*320
   5-fold quotients : {4,2,4,4}*256
   8-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   10-fold quotients : {2,2,4,4}*128, {4,2,2,4}*128, {4,2,4,2}*128
   16-fold quotients : {2,2,5,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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