Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(768,150681)
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)( 8,27)( 9,26)(10,25)(11,24)(12,29)(13,28)(14,31)(15,30)(16,34)(17,35)(18,32)(19,33)(36,52)(37,53)(38,54)(39,55)(40,59)(41,58)(42,57)(43,56)(44,61)(45,60)(46,63)(47,62)(48,66)(49,67)(50,64)(51,65);;
s3 := ( 8,11)( 9,10)(12,14)(13,15)(16,17)(18,19)(20,24)(21,25)(22,26)(23,27)(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,46)(39,47)(40,51)(41,50)(42,49)(43,48)(52,65)(53,64)(54,67)(55,66)(56,61)(57,60)(58,63)(59,62);;
s4 := ( 4,36)( 5,37)( 6,38)( 7,39)( 8,41)( 9,40)(10,43)(11,42)(12,46)(13,47)(14,44)(15,45)(16,51)(17,50)(18,49)(19,48)(20,52)(21,53)(22,54)(23,55)(24,57)(25,56)(26,59)(27,58)(28,62)(29,63)(30,60)(31,61)(32,67)(33,66)(34,65)(35,64);;
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*s2*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3 ];;
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)( 8,27)( 9,26)(10,25)(11,24)(12,29)(13,28)(14,31)(15,30)(16,34)(17,35)(18,32)(19,33)(36,52)(37,53)(38,54)(39,55)(40,59)(41,58)(42,57)(43,56)(44,61)(45,60)(46,63)(47,62)(48,66)(49,67)(50,64)(51,65);
s3 := Sym(67)!( 8,11)( 9,10)(12,14)(13,15)(16,17)(18,19)(20,24)(21,25)(22,26)(23,27)(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,46)(39,47)(40,51)(41,50)(42,49)(43,48)(52,65)(53,64)(54,67)(55,66)(56,61)(57,60)(58,63)(59,62);
s4 := Sym(67)!( 4,36)( 5,37)( 6,38)( 7,39)( 8,41)( 9,40)(10,43)(11,42)(12,46)(13,47)(14,44)(15,45)(16,51)(17,50)(18,49)(19,48)(20,52)(21,53)(22,54)(23,55)(24,57)(25,56)(26,59)(27,58)(28,62)(29,63)(30,60)(31,61)(32,67)(33,66)(34,65)(35,64);
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*s2*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3 >;