Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1792,1076197)
Rank
6
Schläfli Type
{2,2,4,4,14}
Vertices, edges, …
2, 2, 4, 8, 28, 14
Order of s0s1s2s3s4s5
28
Order of s0s1s2s3s4s5s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)(50,57)(51,58)(52,59)(53,60);;
s3 := ( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60);;
s4 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);;
s5 := ( 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,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(60)!(1,2);
s1 := Sym(60)!(3,4);
s2 := Sym(60)!(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)(50,57)(51,58)(52,59)(53,60);
s3 := Sym(60)!( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60);
s4 := Sym(60)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);
s5 := 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,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;