Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {4,2,4,12}*768b

Overview

Group
SmallGroup(768,1088766)
Rank
5
Schläfli Type
{4,2,4,12}
Vertices, edges, …
4, 4, 4, 24, 12
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

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

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