Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {5,2,16,4}*1280a

Overview

Group
SmallGroup(1280,323301)
Rank
5
Schläfli Type
{5,2,16,4}
Vertices, edges, …
5, 5, 16, 32, 4
Order of s0s1s2s3s4
80
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 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);;
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 := ( 6,22)( 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);;
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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(69)!(2,3)(4,5);
s1 := Sym(69)!(1,2)(3,4);
s2 := 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);
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)!( 6,22)( 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);
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;