Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,2,4,12}

Atlas Canonical Name {5,2,2,4,12}*1920c

Overview

Group
SmallGroup(1920,240141)
Rank
6
Schläfli Type
{5,2,2,4,12}
Vertices, edges, …
5, 5, 2, 4, 24, 12
Order of s0s1s2s3s4s5
60
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

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