Overview
- Group
- SmallGroup(480,948)
- Rank
- 3
- Schläfli Type
- {10,6}
- Vertices, edges, …
- 40, 120, 24
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3,17)( 4,13)( 7,16)( 8,15)( 9,26)(10,14)(11,39)(12,28)(18,33)(19,34)(20,30)(21,37)(22,38)(23,29)(24,40)(25,27)(31,36)(32,35);; s1 := ( 1, 9)( 2,10)( 3, 5)( 4, 6)( 7,20)( 8,23)(11,26)(12,14)(13,25)(15,21)(16,22)(17,24)(18,38)(19,29)(27,39)(28,40)(30,36)(35,37);; s2 := ( 2, 5)( 3,13)( 4,17)( 7, 8)( 9,14)(10,26)(11,38)(12,37)(15,16)(18,36)(20,27)(21,28)(22,39)(23,40)(24,29)(25,30)(31,33);; 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*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!( 3,17)( 4,13)( 7,16)( 8,15)( 9,26)(10,14)(11,39)(12,28)(18,33)(19,34)(20,30)(21,37)(22,38)(23,29)(24,40)(25,27)(31,36)(32,35); s1 := Sym(40)!( 1, 9)( 2,10)( 3, 5)( 4, 6)( 7,20)( 8,23)(11,26)(12,14)(13,25)(15,21)(16,22)(17,24)(18,38)(19,29)(27,39)(28,40)(30,36)(35,37); s2 := Sym(40)!( 2, 5)( 3,13)( 4,17)( 7, 8)( 9,14)(10,26)(11,38)(12,37)(15,16)(18,36)(20,27)(21,28)(22,39)(23,40)(24,29)(25,30)(31,33); poly := sub<Sym(40)|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*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1 >;
References
None.
to this polytope.