Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,4,4,6}

Atlas Canonical Name {5,2,4,4,6}*1920

Overview

Group
SmallGroup(1920,205028)
Rank
6
Schläfli Type
{5,2,4,4,6}
Vertices, edges, …
5, 5, 4, 8, 12, 6
Order of s0s1s2s3s4s5
60
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

3-fold

4-fold

6-fold

8-fold

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

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