Polytope of Type {15,12} with group SmallGroup(1440,4642)

Overview

Group: SmallGroup(1440,4642)
Rank: 3
Schläfli Type: {15,12}
Vertices, edges, …: 60, 360, 48
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 60
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{15,6}*720d

3-fold

{5,12}*480

4-fold

{15,3}*360

6-fold

{5,6}*240b

12-fold

24-fold

{5,3}*60

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)(50,51);;
s1 := ( 2,23)( 3,39)( 4,33)( 5,17)( 6, 7)( 8,20)( 9,22)(10,34)(11,29)(12,16)(13,24)(14,26)(15,41)(18,32)(19,48)(25,44)(27,38)(36,40)(42,46)(43,47)(49,50);;
s2 := ( 1, 4)( 2,35)( 3, 5)( 6,25)( 7,27)( 8,29)( 9,46)(10,24)(11,47)(12,37)(13,30)(14,23)(15,31)(16,42)(17,48)(18,38)(19,21)(20,26)(22,36)(28,32)(33,44)(34,39)(40,41)(43,45)(50,51);;
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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References