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

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

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