Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,3,12}*384

Overview

Group
SmallGroup(384,20062)
Rank
5
Schläfli Type
{2,2,3,12}
Vertices, edges, …
2, 2, 4, 24, 16
Order of s0s1s2s3s4
8
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

5-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,23)(11,26)(13,18)(14,17)(15,35)(16,38)(19,41)(20,42)(21,27)(22,24)(25,46)(28,45)(29,30)(31,47)(32,49)(33,36)(34,39)(37,51)(40,52)(43,44);;
s3 := ( 5, 8)( 6,17)( 7,13)(10,46)(11,45)(12,29)(14,18)(15,51)(16,52)(19,44)(20,43)(21,28)(22,25)(23,24)(26,27)(31,48)(32,50)(33,37)(34,40)(35,36)(38,39)(41,42);;
s4 := ( 5,48)( 6,43)( 7,44)( 8,37)( 9,51)(10,16)(11,15)(12,50)(13,25)(14,45)(17,28)(18,46)(19,34)(20,33)(21,32)(22,31)(23,38)(24,47)(26,35)(27,49)(29,40)(30,52)(36,42)(39,41);;
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*s1*s0*s1, 
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, 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(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 6, 7)( 8, 9)(10,23)(11,26)(13,18)(14,17)(15,35)(16,38)(19,41)(20,42)(21,27)(22,24)(25,46)(28,45)(29,30)(31,47)(32,49)(33,36)(34,39)(37,51)(40,52)(43,44);
s3 := Sym(52)!( 5, 8)( 6,17)( 7,13)(10,46)(11,45)(12,29)(14,18)(15,51)(16,52)(19,44)(20,43)(21,28)(22,25)(23,24)(26,27)(31,48)(32,50)(33,37)(34,40)(35,36)(38,39)(41,42);
s4 := Sym(52)!( 5,48)( 6,43)( 7,44)( 8,37)( 9,51)(10,16)(11,15)(12,50)(13,25)(14,45)(17,28)(18,46)(19,34)(20,33)(21,32)(22,31)(23,38)(24,47)(26,35)(27,49)(29,40)(30,52)(36,42)(39,41);
poly := sub<Sym(52)|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*s1*s0*s1, 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, 
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3 >;