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