Overview
- Group
- SmallGroup(1728,30201)
- Rank
- 5
- Schläfli Type
- {9,2,8,3}
- Vertices, edges, …
- 9, 9, 16, 24, 6
- 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 := (10,20)(11,16)(12,15)(13,36)(14,38)(17,21)(18,25)(19,27)(22,24)(23,26)(28,53)(29,57)(30,52)(31,55)(32,56)(33,54)(34,37)(35,39)(40,48)(41,50)(42,46)(43,49)(44,51)(45,47);; s3 := (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);; s4 := (10,14)(11,23)(12,19)(15,27)(16,26)(17,35)(18,22)(20,38)(21,39)(24,25)(28,30)(29,51)(31,33)(32,50)(40,42)(41,56)(43,45)(44,57)(46,48)(47,49)(52,53)(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,
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!(10,20)(11,16)(12,15)(13,36)(14,38)(17,21)(18,25)(19,27)(22,24)(23,26)(28,53)(29,57)(30,52)(31,55)(32,56)(33,54)(34,37)(35,39)(40,48)(41,50)(42,46)(43,49)(44,51)(45,47); s3 := 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); s4 := Sym(57)!(10,14)(11,23)(12,19)(15,27)(16,26)(17,35)(18,22)(20,38)(21,39)(24,25)(28,30)(29,51)(31,33)(32,50)(40,42)(41,56)(43,45)(44,57)(46,48)(47,49)(52,53)(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, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;