Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,14}

Atlas Canonical Name {2,8,14}*448

Overview

Group
SmallGroup(448,1207)
Rank
4
Schläfli Type
{2,8,14}
Vertices, edges, …
2, 8, 56, 14
Order of s0s1s2s3
56
Order of s0s1s2s3s2s1
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

28-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

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