Overview
- Group
- SmallGroup(960,8239)
- Rank
- 5
- Schläfli Type
- {3,2,8,10}
- Vertices, edges, …
- 3, 3, 8, 40, 10
- Order of s0s1s2s3s4
- 120
- 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
4-fold
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (14,19)(15,20)(16,21)(17,22)(18,23)(24,39)(25,40)(26,41)(27,42)(28,43)(29,34)(30,35)(31,36)(32,37)(33,38);; s3 := ( 4,24)( 5,28)( 6,27)( 7,26)( 8,25)( 9,29)(10,33)(11,32)(12,31)(13,30)(14,39)(15,43)(16,42)(17,41)(18,40)(19,34)(20,38)(21,37)(22,36)(23,35);; s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43);; 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,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*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(43)!(2,3); s1 := Sym(43)!(1,2); s2 := Sym(43)!(14,19)(15,20)(16,21)(17,22)(18,23)(24,39)(25,40)(26,41)(27,42)(28,43)(29,34)(30,35)(31,36)(32,37)(33,38); s3 := Sym(43)!( 4,24)( 5,28)( 6,27)( 7,26)( 8,25)( 9,29)(10,33)(11,32)(12,31)(13,30)(14,39)(15,43)(16,42)(17,41)(18,40)(19,34)(20,38)(21,37)(22,36)(23,35); s4 := Sym(43)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43); poly := sub<Sym(43)|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, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;