Polytope of Type {44,2} with group SmallGroup(176,29)

Overview

Group: SmallGroup(176,29)
Rank: 3
Schläfli Type: {44,2}
Vertices, edges, …: 44, 44, 2
Order of s₀s₁s₂: 44
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

{22,2}*88

4-fold

{11,2}*44

11-fold

{4,2}*16

22-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 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)(38,41)(42,44);;
s2 := (45,46);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(46)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44);
s1 := Sym(46)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)(38,41)(42,44);
s2 := Sym(46)!(45,46);
poly := sub<Sym(46)|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*s0*s1*s0*s1 >;