Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,70}

Atlas Canonical Name {2,70}*280

Overview

Group
SmallGroup(280,39)
Rank
3
Schläfli Type
{2,70}
Vertices, edges, …
2, 70, 70
Order of s0s1s2
70
Order of s0s1s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

5-fold

7-fold

10-fold

14-fold

35-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(10,31)(11,37)(12,36)(13,35)(14,34)(15,33)(16,32)(17,24)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(39,44)(40,43)(41,42)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60);;
s2 := ( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,39)(11,38)(12,44)(13,43)(14,42)(15,41)(16,40)(17,67)(18,66)(19,72)(20,71)(21,70)(22,69)(23,68)(24,60)(25,59)(26,65)(27,64)(28,63)(29,62)(30,61)(31,53)(32,52)(33,58)(34,57)(35,56)(36,55)(37,54);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(72)!(1,2);
s1 := Sym(72)!( 4, 9)( 5, 8)( 6, 7)(10,31)(11,37)(12,36)(13,35)(14,34)(15,33)(16,32)(17,24)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(39,44)(40,43)(41,42)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60);
s2 := Sym(72)!( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,39)(11,38)(12,44)(13,43)(14,42)(15,41)(16,40)(17,67)(18,66)(19,72)(20,71)(21,70)(22,69)(23,68)(24,60)(25,59)(26,65)(27,64)(28,63)(29,62)(30,61)(31,53)(32,52)(33,58)(34,57)(35,56)(36,55)(37,54);
poly := sub<Sym(72)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;