Polytope of Type {5,2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,16}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323301)
Rank : 5
Schlafli Type : {5,2,4,16}
Number of vertices, edges, etc : 5, 5, 4, 32, 16
Order of s₀s₁s₂s₃s₄ : 80
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 : {5,2,4,8}*640a, {5,2,2,16}*640
   4-fold quotients : {5,2,4,4}*320, {5,2,2,8}*320
   8-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
   16-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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