Overview
- Group
- SmallGroup(864,3999)
- Rank
- 6
- Schläfli Type
- {3,2,4,9,2}
- Vertices, edges, …
- 3, 3, 4, 18, 9, 2
- Order of s0s1s2s3s4s5
- 18
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)(30,37)(32,38);; s3 := ( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);; s4 := ( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);; s5 := (40,41);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s2*s3, 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(41)!(2,3); s1 := Sym(41)!(1,2); s2 := Sym(41)!( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)(30,37)(32,38); s3 := Sym(41)!( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38); s4 := Sym(41)!( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38); s5 := Sym(41)!(40,41); poly := sub<Sym(41)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;