Overview
- Group
- SmallGroup(576,5012)
- Rank
- 5
- Schläfli Type
- {2,2,18,4}
- Vertices, edges, …
- 2, 2, 18, 36, 4
- 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
9-fold
12-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 8,12)( 9,11)(10,13)(15,16)(17,21)(18,20)(19,22)(24,25)(26,30)(27,29)(28,31)(33,34)(35,39)(36,38)(37,40);; s3 := ( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,35)(24,37)(25,36)(26,32)(27,34)(28,33)(29,39)(30,38)(31,40);; s4 := ( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40);; 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*s1*s0*s1,
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*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!(1,2); s1 := Sym(40)!(3,4); s2 := Sym(40)!( 6, 7)( 8,12)( 9,11)(10,13)(15,16)(17,21)(18,20)(19,22)(24,25)(26,30)(27,29)(28,31)(33,34)(35,39)(36,38)(37,40); s3 := Sym(40)!( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,35)(24,37)(25,36)(26,32)(27,34)(28,33)(29,39)(30,38)(31,40); s4 := Sym(40)!( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40); 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*s1*s0*s1, 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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;