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