Overview
- Group
- SmallGroup(960,5719)
- Rank
- 3
- Schläfli Type
- {4,20}
- Vertices, edges, …
- 24, 240, 120
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 6
- 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
8-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,12)( 2,10)( 3,15)( 4,37)( 5,44)( 6,20)( 7,17)( 8,48)( 9,29)(11,21)(13,28)(14,40)(16,41)(18,46)(19,32)(22,26)(23,25)(24,31)(27,39)(30,45)(33,38)(34,47)(35,36)(42,43);; s1 := ( 1, 3)( 2,21)( 4,48)( 5,32)( 6, 9)( 7,40)( 8,14)(10,36)(11,25)(12,20)(13,39)(15,29)(16,31)(17,37)(18,38)(19,33)(22,47)(23,35)(24,43)(26,34)(27,28)(30,42)(41,45)(44,46);; s2 := ( 1, 8)( 2,43)( 4,30)( 5,13)( 6,24)( 7,47)( 9,22)(10,42)(11,38)(12,48)(16,32)(17,34)(19,41)(20,31)(21,33)(26,29)(27,36)(28,44)(35,39)(37,45);; 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*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 1,12)( 2,10)( 3,15)( 4,37)( 5,44)( 6,20)( 7,17)( 8,48)( 9,29)(11,21)(13,28)(14,40)(16,41)(18,46)(19,32)(22,26)(23,25)(24,31)(27,39)(30,45)(33,38)(34,47)(35,36)(42,43); s1 := Sym(48)!( 1, 3)( 2,21)( 4,48)( 5,32)( 6, 9)( 7,40)( 8,14)(10,36)(11,25)(12,20)(13,39)(15,29)(16,31)(17,37)(18,38)(19,33)(22,47)(23,35)(24,43)(26,34)(27,28)(30,42)(41,45)(44,46); s2 := Sym(48)!( 1, 8)( 2,43)( 4,30)( 5,13)( 6,24)( 7,47)( 9,22)(10,42)(11,38)(12,48)(16,32)(17,34)(19,41)(20,31)(21,33)(26,29)(27,36)(28,44)(35,39)(37,45); 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*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.