Polytope of Type {6,10} with group SmallGroup(120,42)

Overview

Group: SmallGroup(120,42)
Rank: 3
Schläfli Type: {6,10}
Vertices, edges, …: 6, 30, 10
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 2
Also known as: {6,10|2}. if this polytope has another 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

{2,10}*40

5-fold

{6,2}*24

6-fold

{2,5}*20

10-fold

{3,2}*12

15-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

12-fold

13-fold

14-fold

15-fold

16-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);;
s1 := ( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30);;
s2 := ( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);;
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*s1*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(30)!( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);
s1 := Sym(30)!( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30);
s2 := Sym(30)!( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);
poly := sub<Sym(30)|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*s1*s0*s1*s2*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 >;

References