Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,14,10}

Atlas Canonical Name {2,14,10}*560

Overview

Group
SmallGroup(560,176)
Rank
4
Schläfli Type
{2,14,10}
Vertices, edges, …
2, 14, 70, 10
Order of s0s1s2s3
70
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

7-fold

10-fold

14-fold

35-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70);;
s2 := ( 3, 4)( 5, 9)( 6, 8)(10,32)(11,31)(12,37)(13,36)(14,35)(15,34)(16,33)(17,25)(18,24)(19,30)(20,29)(21,28)(22,27)(23,26)(38,39)(40,44)(41,43)(45,67)(46,66)(47,72)(48,71)(49,70)(50,69)(51,68)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);;
s3 := ( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,66)(18,67)(19,68)(20,69)(21,70)(22,71)(23,72)(24,59)(25,60)(26,61)(27,62)(28,63)(29,64)(30,65)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70);
s2 := Sym(72)!( 3, 4)( 5, 9)( 6, 8)(10,32)(11,31)(12,37)(13,36)(14,35)(15,34)(16,33)(17,25)(18,24)(19,30)(20,29)(21,28)(22,27)(23,26)(38,39)(40,44)(41,43)(45,67)(46,66)(47,72)(48,71)(49,70)(50,69)(51,68)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);
s3 := Sym(72)!( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,66)(18,67)(19,68)(20,69)(21,70)(22,71)(23,72)(24,59)(25,60)(26,61)(27,62)(28,63)(29,64)(30,65)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58);
poly := sub<Sym(72)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;