Overview
- Group
- SmallGroup(576,4970)
- Rank
- 5
- Schläfli Type
- {4,9,2,4}
- Vertices, edges, …
- 4, 18, 9, 4, 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
6-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 9)( 4,11)( 5,13)( 8,18)(10,20)(14,24)(21,30)(23,32)(25,33)(27,34)(29,35);; s1 := ( 1, 2)( 3, 6)( 4, 5)( 7,15)( 8,14)( 9,16)(10,12)(11,13)(17,23)(18,24)(19,21)(20,22)(25,31)(26,32)(27,29)(28,30)(33,36)(34,35);; s2 := ( 1, 6)( 2, 4)( 3,14)( 5,10)( 7,11)( 8,23)( 9,24)(12,19)(13,20)(15,16)(17,31)(18,32)(21,27)(22,28)(25,29)(26,36)(30,34)(33,35);; s3 := (38,39);; s4 := (37,38)(39,40);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!( 2, 7)( 3, 9)( 4,11)( 5,13)( 8,18)(10,20)(14,24)(21,30)(23,32)(25,33)(27,34)(29,35); s1 := Sym(40)!( 1, 2)( 3, 6)( 4, 5)( 7,15)( 8,14)( 9,16)(10,12)(11,13)(17,23)(18,24)(19,21)(20,22)(25,31)(26,32)(27,29)(28,30)(33,36)(34,35); s2 := Sym(40)!( 1, 6)( 2, 4)( 3,14)( 5,10)( 7,11)( 8,23)( 9,24)(12,19)(13,20)(15,16)(17,31)(18,32)(21,27)(22,28)(25,29)(26,36)(30,34)(33,35); s3 := Sym(40)!(38,39); s4 := Sym(40)!(37,38)(39,40); poly := sub<Sym(40)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;