Polytope of Type {4,30} with group SmallGroup(240,179)

Overview

Group: SmallGroup(240,179)
Rank: 3
Schläfli Type: {4,30}
Vertices, edges, …: 4, 60, 30
Order of s₀s₁s₂: 60
Order of s₀s₁s₂s₁: 2
Also known as: {4,30|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

2-fold

{2,30}*120

3-fold

{4,10}*80

4-fold

{2,15}*60

5-fold

{4,6}*48a

6-fold

{2,10}*40

10-fold

{2,6}*24

12-fold

{2,5}*20

15-fold

{4,2}*16

20-fold

{2,3}*12

30-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60);;
s1 := ( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)(10,42)(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)(21,56)(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52);;
s2 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)(18,25)(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)(43,45)(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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(60)!(31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60);
s1 := Sym(60)!( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)(10,42)(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)(21,56)(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52);
s2 := Sym(60)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)(18,25)(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)(43,45)(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60);
poly := sub<Sym(60)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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