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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20,2}*640
if this polytope has a name.
Group : SmallGroup(640,19674)
Rank : 5
Schlafli Type : {2,4,20,2}
Number of vertices, edges, etc : 2, 4, 40, 20, 2
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,20,2,2} of size 1280
   {2,4,20,2,3} of size 1920
Vertex Figure Of :
   {2,2,4,20,2} of size 1280
   {3,2,4,20,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,20,2}*320, {2,4,10,2}*320
   4-fold quotients : {2,2,10,2}*160
   5-fold quotients : {2,4,4,2}*128
   8-fold quotients : {2,2,5,2}*80
   10-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,20,2}*1280, {2,4,20,4}*1280, {2,8,20,2}*1280a, {2,4,40,2}*1280a, {2,8,20,2}*1280b, {2,4,40,2}*1280b, {2,4,20,2}*1280
   3-fold covers : {2,4,60,2}*1920a, {2,4,20,6}*1920, {6,4,20,2}*1920, {2,12,20,2}*1920
Permutation Representation (GAP) :

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