Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,2,4,12}*768c

Overview

Group
SmallGroup(768,1090143)
Rank
6
Schläfli Type
{2,2,2,4,12}
Vertices, edges, …
2, 2, 2, 4, 24, 12
Order of s0s1s2s3s4s5
12
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 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,27)( 8,19)( 9,16)(10,41)(11,42)(12,13)(14,33)(15,34)(17,28)(18,29)(20,25)(21,26)(22,53)(23,54)(24,52)(30,48)(31,50)(32,46)(35,51)(36,49)(37,47)(38,45)(39,43)(40,44);;
s4 := ( 8, 9)(10,11)(12,22)(14,18)(15,17)(16,30)(19,35)(20,38)(21,23)(24,40)(25,26)(27,43)(28,46)(29,36)(31,34)(32,50)(33,47)(37,49)(41,52)(42,44)(45,54)(48,51);;
s5 := ( 7,15)( 8,11)( 9,26)(10,14)(12,29)(13,18)(16,21)(17,25)(19,42)(20,28)(22,32)(23,49)(24,35)(27,34)(30,45)(31,40)(33,41)(36,54)(37,43)(38,48)(39,47)(44,50)(46,53)(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*s1*s0*s1, 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, 
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(54)!(1,2);
s1 := Sym(54)!(3,4);
s2 := Sym(54)!(5,6);
s3 := Sym(54)!( 7,27)( 8,19)( 9,16)(10,41)(11,42)(12,13)(14,33)(15,34)(17,28)(18,29)(20,25)(21,26)(22,53)(23,54)(24,52)(30,48)(31,50)(32,46)(35,51)(36,49)(37,47)(38,45)(39,43)(40,44);
s4 := Sym(54)!( 8, 9)(10,11)(12,22)(14,18)(15,17)(16,30)(19,35)(20,38)(21,23)(24,40)(25,26)(27,43)(28,46)(29,36)(31,34)(32,50)(33,47)(37,49)(41,52)(42,44)(45,54)(48,51);
s5 := Sym(54)!( 7,15)( 8,11)( 9,26)(10,14)(12,29)(13,18)(16,21)(17,25)(19,42)(20,28)(22,32)(23,49)(24,35)(27,34)(30,45)(31,40)(33,41)(36,54)(37,43)(38,48)(39,47)(44,50)(46,53)(51,52);
poly := sub<Sym(54)|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, 
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, 
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 >;