Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,4}

Atlas Canonical Name {2,12,4}*192c

Overview

Group
SmallGroup(192,1470)
Rank
4
Schläfli Type
{2,12,4}
Vertices, edges, …
2, 12, 24, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
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

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Representations

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