Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(576,8340)
Rank
5
Schläfli Type
{3,2,3,12}
Vertices, edges, …
3, 3, 4, 24, 16
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, 7)( 5,16)( 6,12)( 9,45)(10,44)(11,28)(13,17)(14,50)(15,51)(18,43)(19,42)(20,27)(21,24)(22,23)(25,26)(30,47)(31,49)(32,36)(33,39)(34,35)(37,38)(40,41);;
s4 := ( 4,47)( 5,42)( 6,43)( 7,36)( 8,50)( 9,15)(10,14)(11,49)(12,24)(13,44)(16,27)(17,45)(18,33)(19,32)(20,31)(21,30)(22,37)(23,46)(25,34)(26,48)(28,39)(29,51)(35,41)(38,40);;
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, s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*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, 7)( 5,16)( 6,12)( 9,45)(10,44)(11,28)(13,17)(14,50)(15,51)(18,43)(19,42)(20,27)(21,24)(22,23)(25,26)(30,47)(31,49)(32,36)(33,39)(34,35)(37,38)(40,41);
s4 := Sym(51)!( 4,47)( 5,42)( 6,43)( 7,36)( 8,50)( 9,15)(10,14)(11,49)(12,24)(13,44)(16,27)(17,45)(18,33)(19,32)(20,31)(21,30)(22,37)(23,46)(25,34)(26,48)(28,39)(29,51)(35,41)(38,40);
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, 
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3 >;