Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,3,12,3}*960

Overview

Group
SmallGroup(960,10869)
Rank
5
Schläfli Type
{2,3,12,3}
Vertices, edges, …
2, 5, 40, 40, 5
Order of s0s1s2s3s4
10
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

Representations

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