Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 5
- Schläfli Type
- {2,2,30,6}
- Vertices, edges, …
- 2, 2, 30, 90, 6
- 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 := (3,4);; s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(21,24)(22,23)(25,30)(26,34)(27,33)(28,32)(29,31)(36,39)(37,38)(40,45)(41,49)(42,48)(43,47)(44,46);; s3 := ( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(30,46)(31,45)(32,49)(33,48)(34,47);; s4 := ( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,30)(11,31)(12,32)(13,33)(14,34)(15,25)(16,26)(17,27)(18,28)(19,29)(40,45)(41,46)(42,47)(43,48)(44,49);; 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, s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!(1,2); s1 := Sym(49)!(3,4); s2 := Sym(49)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(21,24)(22,23)(25,30)(26,34)(27,33)(28,32)(29,31)(36,39)(37,38)(40,45)(41,49)(42,48)(43,47)(44,46); s3 := Sym(49)!( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(30,46)(31,45)(32,49)(33,48)(34,47); s4 := Sym(49)!( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,30)(11,31)(12,32)(13,33)(14,34)(15,25)(16,26)(17,27)(18,28)(19,29)(40,45)(41,46)(42,47)(43,48)(44,49); 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, s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 >;