Overview
- Group
- SmallGroup(720,813)
- Rank
- 4
- Schläfli Type
- {6,30,2}
- Vertices, edges, …
- 6, 90, 30, 2
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 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
2-fold
Representations
Permutation Representation (GAP)
s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)(20,35)(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40);; s1 := ( 1,21)( 2,25)( 3,24)( 4,23)( 5,22)( 6,16)( 7,20)( 8,19)( 9,18)(10,17)(11,26)(12,30)(13,29)(14,28)(15,27)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44);; s2 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43);; s3 := (46,47);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(16,31)(17,32)(18,33)(19,34)(20,35)(21,41)(22,42)(23,43)(24,44)(25,45)(26,36)(27,37)(28,38)(29,39)(30,40); s1 := Sym(47)!( 1,21)( 2,25)( 3,24)( 4,23)( 5,22)( 6,16)( 7,20)( 8,19)( 9,18)(10,17)(11,26)(12,30)(13,29)(14,28)(15,27)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44); s2 := Sym(47)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43); s3 := Sym(47)!(46,47); poly := sub<Sym(47)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 >;