Overview
- Group
- SmallGroup(540,54)
- Rank
- 3
- Schläfli Type
- {15,6}
- Vertices, edges, …
- 45, 135, 18
- 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 := ( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(16,31)(17,32)(18,33)(19,43)(20,44)(21,45)(22,40)(23,41)(24,42)(25,37)(26,38)(27,39)(28,34)(29,35)(30,36);; s1 := ( 1,20)( 2,21)( 3,19)( 4,17)( 5,18)( 6,16)( 7,29)( 8,30)( 9,28)(10,26)(11,27)(12,25)(13,23)(14,24)(15,22)(31,34)(32,35)(33,36)(37,43)(38,44)(39,45);; s2 := ( 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);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(16,31)(17,32)(18,33)(19,43)(20,44)(21,45)(22,40)(23,41)(24,42)(25,37)(26,38)(27,39)(28,34)(29,35)(30,36); s1 := Sym(45)!( 1,20)( 2,21)( 3,19)( 4,17)( 5,18)( 6,16)( 7,29)( 8,30)( 9,28)(10,26)(11,27)(12,25)(13,23)(14,24)(15,22)(31,34)(32,35)(33,36)(37,43)(38,44)(39,45); s2 := 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); 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*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.