Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,8,8}

Atlas Canonical Name {5,2,8,8}*1280b

Overview

Group
SmallGroup(1280,145169)
Rank
5
Schläfli Type
{5,2,8,8}
Vertices, edges, …
5, 5, 8, 32, 8
Order of s0s1s2s3s4
40
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 := ( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,31)(15,30)(16,33)(17,32)(18,34)(19,35)(20,36)(21,37)(38,54)(39,55)(40,56)(41,57)(42,59)(43,58)(44,61)(45,60)(46,63)(47,62)(48,65)(49,64)(50,66)(51,67)(52,68)(53,69);;
s3 := (10,11)(12,13)(14,16)(15,17)(18,21)(19,20)(22,26)(23,27)(24,28)(25,29)(30,36)(31,37)(32,34)(33,35)(38,46)(39,47)(40,48)(41,49)(42,51)(43,50)(44,53)(45,52)(54,67)(55,66)(56,69)(57,68)(58,63)(59,62)(60,65)(61,64);;
s4 := ( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,65)(15,64)(16,63)(17,62)(18,69)(19,68)(20,67)(21,66)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,49)(31,48)(32,47)(33,46)(34,53)(35,52)(36,51)(37,50);;
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, 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, 
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)(10,27)(11,26)(12,29)(13,28)(14,31)(15,30)(16,33)(17,32)(18,34)(19,35)(20,36)(21,37)(38,54)(39,55)(40,56)(41,57)(42,59)(43,58)(44,61)(45,60)(46,63)(47,62)(48,65)(49,64)(50,66)(51,67)(52,68)(53,69);
s3 := Sym(69)!(10,11)(12,13)(14,16)(15,17)(18,21)(19,20)(22,26)(23,27)(24,28)(25,29)(30,36)(31,37)(32,34)(33,35)(38,46)(39,47)(40,48)(41,49)(42,51)(43,50)(44,53)(45,52)(54,67)(55,66)(56,69)(57,68)(58,63)(59,62)(60,65)(61,64);
s4 := Sym(69)!( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,65)(15,64)(16,63)(17,62)(18,69)(19,68)(20,67)(21,66)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,49)(31,48)(32,47)(33,46)(34,53)(35,52)(36,51)(37,50);
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, 
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;