Overview
- Group
- SmallGroup(1920,240875)
- Rank
- 3
- Schläfli Type
- {12,20}
- Vertices, edges, …
- 48, 480, 80
- Order of s0s1s2
- 20
- Order of s0s1s2s1
- 20
- 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
16-fold
32-fold
120-fold
240-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 := ( 1,23)( 2,41)( 3,42)( 4,37)( 5,30)( 6,34)( 7,28)( 8,36)( 9,24)(10,29)(11,16)(12,38)(13,14)(15,44)(17,21)(18,19)(20,45)(22,32)(25,27)(26,39)(31,35)(33,47)(40,48)(43,46)(51,52);; s1 := ( 1,12)( 2,35)( 3, 4)( 5,44)( 6,40)( 7,43)( 8,45)( 9,46)(10,48)(11,31)(13,36)(14,15)(16,42)(17,37)(18,30)(19,20)(21,41)(22,47)(23,39)(24,29)(25,38)(26,32)(27,33)(28,34)(49,52)(50,51);; s2 := ( 2,38)( 3,32)( 4,46)( 5,29)( 6,21)( 7,36)( 8,28)( 9,16)(10,30)(11,24)(12,41)(15,20)(17,34)(22,42)(25,26)(27,39)(31,48)(35,40)(37,43)(44,45);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(52)!( 1,23)( 2,41)( 3,42)( 4,37)( 5,30)( 6,34)( 7,28)( 8,36)( 9,24)(10,29)(11,16)(12,38)(13,14)(15,44)(17,21)(18,19)(20,45)(22,32)(25,27)(26,39)(31,35)(33,47)(40,48)(43,46)(51,52); s1 := Sym(52)!( 1,12)( 2,35)( 3, 4)( 5,44)( 6,40)( 7,43)( 8,45)( 9,46)(10,48)(11,31)(13,36)(14,15)(16,42)(17,37)(18,30)(19,20)(21,41)(22,47)(23,39)(24,29)(25,38)(26,32)(27,33)(28,34)(49,52)(50,51); s2 := Sym(52)!( 2,38)( 3,32)( 4,46)( 5,29)( 6,21)( 7,36)( 8,28)( 9,16)(10,30)(11,24)(12,41)(15,20)(17,34)(22,42)(25,26)(27,39)(31,48)(35,40)(37,43)(44,45); poly := sub<Sym(52)|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*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.