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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,16}*1920
if this polytope has a name.
Group : SmallGroup(1920,203901)
Rank : 5
Schlafli Type : {3,2,10,16}
Number of vertices, edges, etc : 3, 3, 10, 80, 16
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 : {3,2,10,8}*960
   4-fold quotients : {3,2,10,4}*480
   5-fold quotients : {3,2,2,16}*384
   8-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,2,8}*192
   16-fold quotients : {3,2,5,2}*120
   20-fold quotients : {3,2,2,4}*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 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)
(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)
(56,57)(60,63)(61,62)(65,68)(66,67)(70,73)(71,72)(75,78)(76,77)(80,83)
(81,82);;
s3 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,35)
(25,34)(26,38)(27,37)(28,36)(29,40)(30,39)(31,43)(32,42)(33,41)(44,65)(45,64)
(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,80)(55,79)(56,83)
(57,82)(58,81)(59,75)(60,74)(61,78)(62,77)(63,76);;
s4 := ( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)
(14,59)(15,60)(16,61)(17,62)(18,63)(19,54)(20,55)(21,56)(22,57)(23,58)(24,74)
(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,64)(35,65)
(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope