Overview
- Group
- SmallGroup(140,10)
- Rank
- 2
- Schläfli Type
- {70}
- Vertices, edges, …
- 70, 70
- Order of s0s1
- 70
- Also known as
- 70-gon, {70}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
5-fold
7-fold
10-fold
14-fold
35-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
9-fold
10-fold
11-fold
12-fold
13-fold
14-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,29)( 9,35)(10,34)(11,33)(12,32)(13,31)(14,30)(15,22)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(37,42)(38,41)(39,40)(43,64)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58);; s1 := ( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)(21,66)(22,58)(23,57)(24,63)(25,62)(26,61)(27,60)(28,59)(29,51)(30,50)(31,56)(32,55)(33,54)(34,53)(35,52);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*s0*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*s0*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*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(70)!( 2, 7)( 3, 6)( 4, 5)( 8,29)( 9,35)(10,34)(11,33)(12,32)(13,31)(14,30)(15,22)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(37,42)(38,41)(39,40)(43,64)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58); s1 := Sym(70)!( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)(21,66)(22,58)(23,57)(24,63)(25,62)(26,61)(27,60)(28,59)(29,51)(30,50)(31,56)(32,55)(33,54)(34,53)(35,52); poly := sub<Sym(70)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*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*s0*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*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.