Polytope of Type {15,8} with group SmallGroup(1440,4612)

Overview

Group: SmallGroup(1440,4612)
Rank: 3
Schläfli Type: {15,8}
Vertices, edges, …: 90, 360, 48
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{15,4}*720

3-fold

{5,8}*480

6-fold

{5,4}*240

12-fold

{5,4}*120

120-fold

{3,2}*12

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, 7)( 6, 8)( 9,12)(10,11)(13,37)(14,39)(15,38)(16,40)(17,21)(18,22)(19,23)(20,24)(25,33)(26,35)(27,34)(28,36)(29,32)(30,31);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*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, 7)( 6, 8)( 9,12)(10,11)(13,37)(14,39)(15,38)(16,40)(17,21)(18,22)(19,23)(20,24)(25,33)(26,35)(27,34)(28,36)(29,32)(30,31);
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1 >;

References