Polytope of Type {2,42} with group SmallGroup(168,56)

Overview

Group: SmallGroup(168,56)
Rank: 3
Schläfli Type: {2,42}
Vertices, edges, …: 2, 42, 42
Order of s₀s₁s₂: 42
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,21}*84

3-fold

{2,14}*56

6-fold

{2,7}*28

7-fold

{2,6}*24

14-fold

{2,3}*12

21-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,44)(42,43);;
s2 := ( 3,19)( 4,13)( 5,11)( 6,21)( 7, 9)( 8,31)(10,15)(12,25)(14,23)(16,33)(17,20)(18,41)(22,27)(24,37)(26,35)(28,43)(29,32)(30,42)(34,39)(36,38)(40,44);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;