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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,2,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,364865)
Rank : 5
Schlafli Type : {20,4,2,4}
Number of vertices, edges, etc : 20, 40, 4, 4, 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 : {20,4,2,2}*640, {20,2,2,4}*640, {10,4,2,4}*640
   4-fold quotients : {20,2,2,2}*320, {10,2,2,4}*320, {10,4,2,2}*320
   5-fold quotients : {4,4,2,4}*256
   8-fold quotients : {5,2,2,4}*160, {10,2,2,2}*160
   10-fold quotients : {4,4,2,2}*128, {2,4,2,4}*128, {4,2,2,4}*128
   16-fold quotients : {5,2,2,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,4,2,2}*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, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(21,31)(22,35)
(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44)(47,50)
(48,49)(52,55)(53,54)(57,60)(58,59)(61,71)(62,75)(63,74)(64,73)(65,72)(66,76)
(67,80)(68,79)(69,78)(70,77);;
s1 := ( 1,22)( 2,21)( 3,25)( 4,24)( 5,23)( 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)(41,62)
(42,61)(43,65)(44,64)(45,63)(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);;
s2 := ( 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);;
s3 := (82,83);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(84)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(21,31)
(22,35)(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44)
(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(61,71)(62,75)(63,74)(64,73)(65,72)
(66,76)(67,80)(68,79)(69,78)(70,77);
s1 := Sym(84)!( 1,22)( 2,21)( 3,25)( 4,24)( 5,23)( 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)
(41,62)(42,61)(43,65)(44,64)(45,63)(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);
s2 := Sym(84)!( 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);
s3 := Sym(84)!(82,83);
s4 := Sym(84)!(81,82)(83,84);
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, 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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope