Polytope of Type {15,6} with group SmallGroup(1440,4612)

Overview

Group: SmallGroup(1440,4612)
Rank: 3
Schläfli Type: {15,6}
Vertices, edges, …: 120, 360, 48
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 24
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}*720b

3-fold

{5,6}*480

6-fold

{5,6}*240a

12-fold

{5,6}*120a

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References