Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,8,14}

Atlas Canonical Name {4,2,8,14}*1792

Overview

Group
SmallGroup(1792,1044755)
Rank
5
Schläfli Type
{4,2,8,14}
Vertices, edges, …
4, 4, 8, 56, 14
Order of s0s1s2s3s4
56
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

7-fold

8-fold

14-fold

16-fold

28-fold

56-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)(46,60);;
s3 := ( 5,33)( 6,39)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,40)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48);;
s4 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)(54,55)(56,60)(57,59);;
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*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(60)!(2,3);
s1 := Sym(60)!(1,2)(3,4);
s2 := Sym(60)!(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)(46,60);
s3 := Sym(60)!( 5,33)( 6,39)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,40)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48);
s4 := Sym(60)!( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)(54,55)(56,60)(57,59);
poly := sub<Sym(60)|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*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;