Overview
- Group
- SmallGroup(1728,30201)
- Rank
- 5
- Schläfli Type
- {9,2,3,8}
- Vertices, edges, …
- 9, 9, 6, 24, 16
- Order of s0s1s2s3s4
- 36
- Order of s0s1s2s3s4s3s2s1
- 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
6-fold
8-fold
12-fold
24-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)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)(25,47)(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)(45,57)(48,49);; s3 := (10,13)(11,22)(12,18)(15,51)(16,50)(17,34)(19,23)(20,56)(21,57)(24,49)(25,48)(26,33)(27,30)(28,29)(31,32)(36,53)(37,55)(38,42)(39,45)(40,41)(43,44)(46,47);; s4 := (10,53)(11,49)(12,48)(13,56)(14,42)(15,43)(16,40)(17,55)(18,51)(19,33)(20,31)(21,28)(22,50)(23,30)(24,44)(25,41)(26,54)(27,52)(29,36)(32,37)(34,57)(35,45)(38,47)(39,46);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
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(57)!(2,3)(4,5)(6,7)(8,9); s1 := Sym(57)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(57)!(11,12)(13,14)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)(25,47)(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)(45,57)(48,49); s3 := Sym(57)!(10,13)(11,22)(12,18)(15,51)(16,50)(17,34)(19,23)(20,56)(21,57)(24,49)(25,48)(26,33)(27,30)(28,29)(31,32)(36,53)(37,55)(38,42)(39,45)(40,41)(43,44)(46,47); s4 := Sym(57)!(10,53)(11,49)(12,48)(13,56)(14,42)(15,43)(16,40)(17,55)(18,51)(19,33)(20,31)(21,28)(22,50)(23,30)(24,44)(25,41)(26,54)(27,52)(29,36)(32,37)(34,57)(35,45)(38,47)(39,46); poly := sub<Sym(57)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;