Overview
- Group
- SmallGroup(1080,287)
- Rank
- 3
- Schläfli Type
- {30,6}
- Vertices, edges, …
- 90, 270, 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
- Self-Petrie
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 := ( 2, 3)( 4,13)( 5,15)( 6,14)( 7,10)( 8,12)( 9,11)(17,18)(19,28)(20,30)(21,29)(22,25)(23,27)(24,26)(32,33)(34,43)(35,45)(36,44)(37,40)(38,42)(39,41);; s1 := ( 1, 4)( 2, 5)( 3, 6)( 7,13)( 8,14)( 9,15)(16,36)(17,34)(18,35)(19,33)(20,31)(21,32)(22,45)(23,43)(24,44)(25,42)(26,40)(27,41)(28,39)(29,37)(30,38);; s2 := ( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30);; 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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!( 2, 3)( 4,13)( 5,15)( 6,14)( 7,10)( 8,12)( 9,11)(17,18)(19,28)(20,30)(21,29)(22,25)(23,27)(24,26)(32,33)(34,43)(35,45)(36,44)(37,40)(38,42)(39,41); s1 := Sym(45)!( 1, 4)( 2, 5)( 3, 6)( 7,13)( 8,14)( 9,15)(16,36)(17,34)(18,35)(19,33)(20,31)(21,32)(22,45)(23,43)(24,44)(25,42)(26,40)(27,41)(28,39)(29,37)(30,38); s2 := Sym(45)!( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.