Overview
- Group
- SmallGroup(1440,339)
- Rank
- 4
- Schläfli Type
- {9,2,40}
- Vertices, edges, …
- 9, 9, 40, 40
- Order of s0s1s2s3
- 360
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
20-fold
24-fold
30-fold
60-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7)(8,9);; s1 := (1,2)(3,4)(5,6)(7,8);; s2 := (11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,30)(25,29)(26,32)(27,31)(34,39)(35,38)(36,41)(37,40)(42,43)(44,47)(45,46)(48,49);; s3 := (10,16)(11,13)(12,24)(14,26)(15,19)(17,21)(18,34)(20,36)(22,27)(23,29)(25,31)(28,42)(30,44)(32,37)(33,38)(35,40)(39,48)(41,45)(43,46)(47,49);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!(2,3)(4,5)(6,7)(8,9); s1 := Sym(49)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(49)!(11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,30)(25,29)(26,32)(27,31)(34,39)(35,38)(36,41)(37,40)(42,43)(44,47)(45,46)(48,49); s3 := Sym(49)!(10,16)(11,13)(12,24)(14,26)(15,19)(17,21)(18,34)(20,36)(22,27)(23,29)(25,31)(28,42)(30,44)(32,37)(33,38)(35,40)(39,48)(41,45)(43,46)(47,49); poly := sub<Sym(49)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;