Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,39,4}

Atlas Canonical Name {3,2,39,4}*1872

Overview

Group
SmallGroup(1872,1036)
Rank
5
Schläfli Type
{3,2,39,4}
Vertices, edges, …
3, 3, 39, 78, 4
Order of s0s1s2s3s4
39
Order of s0s1s2s3s4s3s2s1
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

None in this atlas.

Representations

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