Overview
- Group
- SmallGroup(1440,4612)
- Rank
- 3
- Schläfli Type
- {6,15}
- Vertices, edges, …
- 48, 360, 120
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 24
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,15)( 2,16)( 3,13)( 4,14)( 7, 8)( 9,28)(10,25)(11,26)(12,27)(17,29)(18,30)(19,32)(20,31)(21,22)(33,36)(37,40)(38,39)(42,43);; s1 := ( 5, 6)( 7, 8)( 9,30)(10,29)(11,32)(12,31)(13,37)(14,39)(15,40)(16,38)(17,34)(18,35)(19,36)(20,33)(21,27)(22,26)(23,28)(24,25)(41,42);; s2 := ( 1,11)( 2,12)( 3,10)( 4, 9)( 5,24)( 6,23)( 7,21)( 8,22)(13,25)(14,28)(15,26)(16,27)(17,32)(18,31)(19,29)(20,30)(37,39)(38,40)(42,43);; 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,
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(43)!( 1,15)( 2,16)( 3,13)( 4,14)( 7, 8)( 9,28)(10,25)(11,26)(12,27)(17,29)(18,30)(19,32)(20,31)(21,22)(33,36)(37,40)(38,39)(42,43); s1 := Sym(43)!( 5, 6)( 7, 8)( 9,30)(10,29)(11,32)(12,31)(13,37)(14,39)(15,40)(16,38)(17,34)(18,35)(19,36)(20,33)(21,27)(22,26)(23,28)(24,25)(41,42); s2 := Sym(43)!( 1,11)( 2,12)( 3,10)( 4, 9)( 5,24)( 6,23)( 7,21)( 8,22)(13,25)(14,28)(15,26)(16,27)(17,32)(18,31)(19,29)(20,30)(37,39)(38,40)(42,43); 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0 >;
References
None.
to this polytope.