Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(576,8340)
Rank
5
Schläfli Type
{3,2,12,3}
Vertices, edges, …
3, 3, 16, 24, 4
Order of s0s1s2s3s4
24
Order of s0s1s2s3s4s3s2s1
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

2-fold

3-fold

Representations

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