Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,8,8}

Atlas Canonical Name {3,2,8,8}*768b

Overview

Group
SmallGroup(768,145169)
Rank
5
Schläfli Type
{3,2,8,8}
Vertices, edges, …
3, 3, 8, 32, 8
Order of s0s1s2s3s4
24
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);;
s1 := (1,2);;
s2 := ( 4,20)( 5,21)( 6,22)( 7,23)( 8,25)( 9,24)(10,27)(11,26)(12,29)(13,28)(14,31)(15,30)(16,32)(17,33)(18,34)(19,35)(36,52)(37,53)(38,54)(39,55)(40,57)(41,56)(42,59)(43,58)(44,61)(45,60)(46,63)(47,62)(48,64)(49,65)(50,66)(51,67);;
s3 := ( 8, 9)(10,11)(12,14)(13,15)(16,19)(17,18)(20,24)(21,25)(22,26)(23,27)(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,46)(39,47)(40,49)(41,48)(42,51)(43,50)(52,65)(53,64)(54,67)(55,66)(56,61)(57,60)(58,63)(59,62);;
s4 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,63)(13,62)(14,61)(15,60)(16,67)(17,66)(18,65)(19,64)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,47)(29,46)(30,45)(31,44)(32,51)(33,50)(34,49)(35,48);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(67)!(2,3);
s1 := Sym(67)!(1,2);
s2 := Sym(67)!( 4,20)( 5,21)( 6,22)( 7,23)( 8,25)( 9,24)(10,27)(11,26)(12,29)(13,28)(14,31)(15,30)(16,32)(17,33)(18,34)(19,35)(36,52)(37,53)(38,54)(39,55)(40,57)(41,56)(42,59)(43,58)(44,61)(45,60)(46,63)(47,62)(48,64)(49,65)(50,66)(51,67);
s3 := Sym(67)!( 8, 9)(10,11)(12,14)(13,15)(16,19)(17,18)(20,24)(21,25)(22,26)(23,27)(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,46)(39,47)(40,49)(41,48)(42,51)(43,50)(52,65)(53,64)(54,67)(55,66)(56,61)(57,60)(58,63)(59,62);
s4 := Sym(67)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,63)(13,62)(14,61)(15,60)(16,67)(17,66)(18,65)(19,64)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,47)(29,46)(30,45)(31,44)(32,51)(33,50)(34,49)(35,48);
poly := sub<Sym(67)|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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;