Overview
- Group
- SmallGroup(784,161)
- Rank
- 3
- Schläfli Type
- {8,8}
- Vertices, edges, …
- 49, 196, 49
- Order of s0s1s2
- 14
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2,32)( 3,14)( 4,38)( 5,20)( 6,44)( 7,26)( 8,34)(10,40)(11,15)(12,46)(13,28)(16,42)(18,48)(19,23)(21,29)(22,37)(24,43)(27,31)(30,45)(35,39)(36,47);; s1 := ( 2, 9)( 3,17)( 4,25)( 5,33)( 6,41)( 7,49)( 8,43)(11,18)(12,26)(13,34)(14,42)(15,36)(16,44)(20,27)(21,35)(22,29)(23,37)(24,45)(31,38)(32,46)(40,47);; s2 := ( 1, 9)( 2,34)( 4,28)( 5,46)( 6,15)( 7,40)( 8,32)(10,26)(11,44)(12,20)(13,38)(16,24)(17,49)(19,36)(21,30)(23,47)(25,41)(27,35)(29,45)(31,39)(42,43);; 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!( 2,32)( 3,14)( 4,38)( 5,20)( 6,44)( 7,26)( 8,34)(10,40)(11,15)(12,46)(13,28)(16,42)(18,48)(19,23)(21,29)(22,37)(24,43)(27,31)(30,45)(35,39)(36,47); s1 := Sym(49)!( 2, 9)( 3,17)( 4,25)( 5,33)( 6,41)( 7,49)( 8,43)(11,18)(12,26)(13,34)(14,42)(15,36)(16,44)(20,27)(21,35)(22,29)(23,37)(24,45)(31,38)(32,46)(40,47); s2 := Sym(49)!( 1, 9)( 2,34)( 4,28)( 5,46)( 6,15)( 7,40)( 8,32)(10,26)(11,44)(12,20)(13,38)(16,24)(17,49)(19,36)(21,30)(23,47)(25,41)(27,35)(29,45)(31,39)(42,43); poly := sub<Sym(49)|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*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2 >;
References
None.
to this polytope.