Overview
- Group
- SmallGroup(1920,235349)
- Rank
- 5
- Schläfli Type
- {2,6,2,40}
- Vertices, edges, …
- 2, 6, 6, 40, 40
- 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
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
16-fold
20-fold
24-fold
30-fold
40-fold
60-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (5,6)(7,8);; s2 := (3,7)(4,5)(6,8);; s3 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)(25,31)(26,30)(33,38)(34,37)(35,40)(36,39)(41,42)(43,46)(44,45)(47,48);; s4 := ( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,33)(19,35)(21,26)(22,28)(24,30)(27,41)(29,43)(31,36)(32,37)(34,39)(38,47)(40,44)(42,45)(46,48);; 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, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(48)!(1,2); s1 := Sym(48)!(5,6)(7,8); s2 := Sym(48)!(3,7)(4,5)(6,8); s3 := Sym(48)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)(25,31)(26,30)(33,38)(34,37)(35,40)(36,39)(41,42)(43,46)(44,45)(47,48); s4 := Sym(48)!( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,33)(19,35)(21,26)(22,28)(24,30)(27,41)(29,43)(31,36)(32,37)(34,39)(38,47)(40,44)(42,45)(46,48); poly := sub<Sym(48)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;