Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12,2,3,2}

Atlas Canonical Name {4,12,2,3,2}*1152b

Overview

Group
SmallGroup(1152,157549)
Rank
6
Schläfli Type
{4,12,2,3,2}
Vertices, edges, …
4, 24, 12, 3, 3, 2
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, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)(12,28)(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)(31,40)(37,47)(38,48)(39,46);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)(38,44)(40,47)(45,46);;
s3 := (50,51);;
s4 := (49,50);;
s5 := (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, 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, s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(53)!( 1, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)(12,28)(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)(31,40)(37,47)(38,48)(39,46);
s1 := Sym(53)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45);
s2 := Sym(53)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)(38,44)(40,47)(45,46);
s3 := Sym(53)!(50,51);
s4 := Sym(53)!(49,50);
s5 := Sym(53)!(52,53);
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, 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, 
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;