Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,39}

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

Overview

Group
SmallGroup(624,245)
Rank
4
Schläfli Type
{2,4,39}
Vertices, edges, …
2, 4, 78, 39
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 := ( 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);;
s2 := ( 4, 5)( 7,51)( 8,53)( 9,52)(10,54)(11,47)(12,49)(13,48)(14,50)(15,43)(16,45)(17,44)(18,46)(19,39)(20,41)(21,40)(22,42)(23,35)(24,37)(25,36)(26,38)(27,31)(28,33)(29,32)(30,34);;
s3 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,51)(12,52)(13,54)(14,53)(15,47)(16,48)(17,50)(18,49)(19,43)(20,44)(21,46)(22,45)(23,39)(24,40)(25,42)(26,41)(27,35)(28,36)(29,38)(30,37)(33,34);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*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*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*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(54)!(1,2);
s1 := 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);
s2 := Sym(54)!( 4, 5)( 7,51)( 8,53)( 9,52)(10,54)(11,47)(12,49)(13,48)(14,50)(15,43)(16,45)(17,44)(18,46)(19,39)(20,41)(21,40)(22,42)(23,35)(24,37)(25,36)(26,38)(27,31)(28,33)(29,32)(30,34);
s3 := Sym(54)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,51)(12,52)(13,54)(14,53)(15,47)(16,48)(17,50)(18,49)(19,43)(20,44)(21,46)(22,45)(23,39)(24,40)(25,42)(26,41)(27,35)(28,36)(29,38)(30,37)(33,34);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;