Polytope of Type {3,2,16,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,16,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,203901)
Rank : 5
Schlafli Type : {3,2,16,10}
Number of vertices, edges, etc : 3, 3, 16, 80, 10
Order of s₀s₁s₂s₃s₄ : 240
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 : {3,2,8,10}*960
   4-fold quotients : {3,2,4,10}*480
   5-fold quotients : {3,2,16,2}*384
   8-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,8,2}*192
   16-fold quotients : {3,2,2,5}*120
   20-fold quotients : {3,2,4,2}*96
   40-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope