Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {3,2,12,4}*576c

Overview

Group
SmallGroup(576,8312)
Rank
5
Schläfli Type
{3,2,12,4}
Vertices, edges, …
3, 3, 12, 24, 4
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
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

2-fold

3-fold

Representations

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