Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1280,145169)
Rank
5
Schläfli Type
{8,8,2,5}
Vertices, edges, …
8, 32, 8, 5, 5
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 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)(48,64);;
s1 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)(20,24)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);;
s2 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,44)(26,43)(27,42)(28,41)(29,48)(30,47)(31,46)(32,45);;
s3 := (66,67)(68,69);;
s4 := (65,66)(67,68);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(69)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)(48,64);
s1 := Sym(69)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)(20,24)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);
s2 := Sym(69)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,44)(26,43)(27,42)(28,41)(29,48)(30,47)(31,46)(32,45);
s3 := Sym(69)!(66,67)(68,69);
s4 := Sym(69)!(65,66)(67,68);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;