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

Overview

Group: SmallGroup(168,56)
Rank: 3
Schläfli Type: {42,2}
Vertices, edges, …: 42, 42, 2
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
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{21,2}*84

3-fold

{14,2}*56

6-fold

{7,2}*28

7-fold

{6,2}*24

14-fold

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

Permutation Representation (Magma)

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