Polytope of Type {30,6} with group SmallGroup(1440,4612)

Overview

Group: SmallGroup(1440,4612)
Rank: 3
Schläfli Type: {30,6}
Vertices, edges, …: 120, 360, 24
Order of s₀s₁s₂: 24
Order of s₀s₁s₂s₁: 8
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}*720a

3-fold

{10,6}*480a

6-fold

{5,6}*240a

12-fold

{5,6}*120a

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

References