Overview
- Group
- SmallGroup(480,959)
- Rank
- 3
- Schläfli Type
- {5,20}
- Vertices, edges, …
- 12, 120, 48
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 12
- 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
8-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 := ( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);; s1 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);; s2 := ( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)(12,29)(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)(36,38)(37,47)(41,42)(45,48);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48); s1 := Sym(48)!( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47); s2 := Sym(48)!( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)(12,29)(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)(36,38)(37,47)(41,42)(45,48); poly := sub<Sym(48)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.