Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,39,4}

Atlas Canonical Name {2,39,4}*624

Overview

Group
SmallGroup(624,245)
Rank
4
Schläfli Type
{2,39,4}
Vertices, edges, …
2, 39, 78, 4
Order of s0s1s2s3
78
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

13-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

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