Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 5
- Schläfli Type
- {2,30,6,2}
- Vertices, edges, …
- 2, 30, 90, 6, 2
- Order of s0s1s2s3s4
- 30
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
10-fold
15-fold
18-fold
30-fold
45-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44);; s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)(32,45);; s3 := ( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47);; s4 := (48,49);; 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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!(1,2); s1 := Sym(49)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44); s2 := Sym(49)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)(32,45); s3 := Sym(49)!( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47); s4 := Sym(49)!(48,49); poly := sub<Sym(49)|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, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;