Overview
- Group
- SmallGroup(784,161)
- Rank
- 3
- Schläfli Type
- {14,8}
- Vertices, edges, …
- 49, 196, 28
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 14
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-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, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30);; s1 := ( 1, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)(47,49);; s2 := ( 2,12)( 3,16)( 4,27)( 5,31)( 6,42)( 7,46)( 8,28)( 9,32)(10,36)(11,47)(14,17)(15,48)(19,22)(20,33)(21,37)(24,34)(25,38)(26,49)(29,39)(30,43)(41,44);; 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*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30); s1 := Sym(49)!( 1, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)(47,49); s2 := Sym(49)!( 2,12)( 3,16)( 4,27)( 5,31)( 6,42)( 7,46)( 8,28)( 9,32)(10,36)(11,47)(14,17)(15,48)(19,22)(20,33)(21,37)(24,34)(25,38)(26,49)(29,39)(30,43)(41,44); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 >;
References
None.
to this polytope.