Overview
- Group
- SmallGroup(1728,30173)
- Rank
- 5
- Schläfli Type
- {9,2,4,12}
- Vertices, edges, …
- 9, 9, 4, 24, 12
- Order of s0s1s2s3s4
- 36
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-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 := (10,15)(11,19)(12,22)(13,23)(14,24)(16,30)(17,31)(18,32)(20,36)(21,37)(25,42)(26,43)(27,41)(28,44)(29,45)(33,54)(34,52)(35,50)(38,51)(39,53)(40,49)(46,56)(47,57)(48,55);; s3 := (11,12)(13,14)(15,25)(17,21)(18,20)(19,33)(22,38)(23,41)(24,26)(27,43)(28,29)(30,46)(31,49)(32,39)(34,37)(35,53)(36,50)(40,52)(44,55)(45,47)(48,57)(51,54);; s4 := (10,18)(11,14)(12,29)(13,17)(15,32)(16,21)(19,24)(20,28)(22,45)(23,31)(25,35)(26,52)(27,38)(30,37)(33,48)(34,43)(36,44)(39,57)(40,46)(41,51)(42,50)(47,53)(49,56)(54,55);; 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*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!(10,15)(11,19)(12,22)(13,23)(14,24)(16,30)(17,31)(18,32)(20,36)(21,37)(25,42)(26,43)(27,41)(28,44)(29,45)(33,54)(34,52)(35,50)(38,51)(39,53)(40,49)(46,56)(47,57)(48,55); s3 := Sym(57)!(11,12)(13,14)(15,25)(17,21)(18,20)(19,33)(22,38)(23,41)(24,26)(27,43)(28,29)(30,46)(31,49)(32,39)(34,37)(35,53)(36,50)(40,52)(44,55)(45,47)(48,57)(51,54); s4 := Sym(57)!(10,18)(11,14)(12,29)(13,17)(15,32)(16,21)(19,24)(20,28)(22,45)(23,31)(25,35)(26,52)(27,38)(30,37)(33,48)(34,43)(36,44)(39,57)(40,46)(41,51)(42,50)(47,53)(49,56)(54,55); 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*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;