Overview
- Group
- SmallGroup(960,5719)
- Rank
- 3
- Schläfli Type
- {24,6}
- Vertices, edges, …
- 80, 240, 20
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 20
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Self-Petrie
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, 3)( 2,37)( 4,32)( 5,44)( 6,19)( 7,17)( 8,14)( 9,29)(10,20)(11,25)(12,31)(13,42)(15,47)(16,27)(18,38)(21,43)(22,45)(23,28)(24,34)(26,40)(30,48)(33,41)(35,36)(39,46);; s1 := ( 1, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)(32,38)(40,42)(45,46);; s2 := ( 1,27)( 2, 5)( 3,16)( 4, 9)( 6,35)( 7,10)( 8,13)(11,34)(12,48)(14,42)(17,20)(18,45)(19,36)(21,33)(22,38)(24,25)(29,32)(30,31)(37,44)(41,43);; 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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 1, 3)( 2,37)( 4,32)( 5,44)( 6,19)( 7,17)( 8,14)( 9,29)(10,20)(11,25)(12,31)(13,42)(15,47)(16,27)(18,38)(21,43)(22,45)(23,28)(24,34)(26,40)(30,48)(33,41)(35,36)(39,46); s1 := Sym(48)!( 1, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)(32,38)(40,42)(45,46); s2 := Sym(48)!( 1,27)( 2, 5)( 3,16)( 4, 9)( 6,35)( 7,10)( 8,13)(11,34)(12,48)(14,42)(17,20)(18,45)(19,36)(21,33)(22,38)(24,25)(29,32)(30,31)(37,44)(41,43); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2 >;
References
None.
to this polytope.