Polytope of Type {6,15} with group SmallGroup(180,29)

Overview

Group: SmallGroup(180,29)
Rank: 3
Schläfli Type: {6,15}
Vertices, edges, …: 6, 45, 15
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{2,15}*60

5-fold

{6,3}*36

9-fold

{2,5}*20

15-fold

{2,3}*12

Covers minimal covers in bold

2-fold

{6,30}*360c

3-fold

4-fold

5-fold

6-fold

7-fold

{6,105}*1260

8-fold

9-fold

10-fold

11-fold

{6,165}*1980

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

References