Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,12,2,5}

Atlas Canonical Name {2,3,12,2,5}*1920

Overview

Group
SmallGroup(1920,240195)
Rank
6
Schläfli Type
{2,3,12,2,5}
Vertices, edges, …
2, 4, 24, 16, 5, 5
Order of s0s1s2s3s4s5
40
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

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

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