Overview
- Group
- SmallGroup(540,54)
- Rank
- 3
- Schläfli Type
- {6,15}
- Vertices, edges, …
- 18, 135, 45
- Order of s0s1s2
- 30
- 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
3-fold
5-fold
9-fold
15-fold
27-fold
45-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45);; s1 := ( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(16,33)(17,31)(18,32)(19,45)(20,43)(21,44)(22,42)(23,40)(24,41)(25,39)(26,37)(27,38)(28,36)(29,34)(30,35);; s2 := ( 1,19)( 2,20)( 3,21)( 4,16)( 5,17)( 6,18)( 7,28)( 8,29)( 9,30)(10,25)(11,26)(12,27)(13,22)(14,23)(15,24)(31,34)(32,35)(33,36)(37,43)(38,44)(39,45);; 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*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
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(45)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45); s1 := Sym(45)!( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(16,33)(17,31)(18,32)(19,45)(20,43)(21,44)(22,42)(23,40)(24,41)(25,39)(26,37)(27,38)(28,36)(29,34)(30,35); s2 := Sym(45)!( 1,19)( 2,20)( 3,21)( 4,16)( 5,17)( 6,18)( 7,28)( 8,29)( 9,30)(10,25)(11,26)(12,27)(13,22)(14,23)(15,24)(31,34)(32,35)(33,36)(37,43)(38,44)(39,45); poly := sub<Sym(45)|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*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 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
None.
to this polytope.