Overview
- Group
- SmallGroup(1728,30173)
- Rank
- 5
- Schläfli Type
- {9,2,12,4}
- Vertices, edges, …
- 9, 9, 12, 24, 4
- 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 := (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);; s3 := (10,17)(11,13)(12,28)(14,18)(15,52)(16,20)(19,43)(21,29)(22,57)(23,51)(24,35)(25,34)(26,38)(27,32)(30,53)(31,42)(33,47)(36,56)(37,48)(39,46)(40,45)(41,50)(44,54)(49,55);; s4 := (10,56)(11,54)(12,51)(13,57)(14,48)(15,46)(16,42)(17,53)(18,40)(19,33)(20,52)(21,35)(22,38)(23,47)(24,55)(25,30)(26,44)(27,29)(28,43)(31,39)(32,49)(34,36)(37,50)(41,45);; 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,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2,
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)(15,25)(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); s3 := Sym(57)!(10,17)(11,13)(12,28)(14,18)(15,52)(16,20)(19,43)(21,29)(22,57)(23,51)(24,35)(25,34)(26,38)(27,32)(30,53)(31,42)(33,47)(36,56)(37,48)(39,46)(40,45)(41,50)(44,54)(49,55); s4 := Sym(57)!(10,56)(11,54)(12,51)(13,57)(14,48)(15,46)(16,42)(17,53)(18,40)(19,33)(20,52)(21,35)(22,38)(23,47)(24,55)(25,30)(26,44)(27,29)(28,43)(31,39)(32,49)(34,36)(37,50)(41,45); 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, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;