Overview
- Group
- SmallGroup(1080,287)
- Rank
- 3
- Schläfli Type
- {6,30}
- Vertices, edges, …
- 18, 270, 90
- 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
10-fold
15-fold
27-fold
30-fold
45-fold
54-fold
90-fold
135-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45);; s1 := ( 1,17)( 2,18)( 3,16)( 4,29)( 5,30)( 6,28)( 7,26)( 8,27)( 9,25)(10,23)(11,24)(12,22)(13,20)(14,21)(15,19)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42);; s2 := ( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,19)(17,21)(18,20)(22,28)(23,30)(24,29)(26,27)(31,34)(32,36)(33,35)(37,43)(38,45)(39,44)(41,42);; 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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45); s1 := Sym(45)!( 1,17)( 2,18)( 3,16)( 4,29)( 5,30)( 6,28)( 7,26)( 8,27)( 9,25)(10,23)(11,24)(12,22)(13,20)(14,21)(15,19)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42); s2 := Sym(45)!( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,19)(17,21)(18,20)(22,28)(23,30)(24,29)(26,27)(31,34)(32,36)(33,35)(37,43)(38,45)(39,44)(41,42); 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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.