Overview
- Group
- SmallGroup(1080,337)
- Rank
- 4
- Schläfli Type
- {2,6,15}
- Vertices, edges, …
- 2, 18, 135, 45
- 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
15-fold
27-fold
45-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);; s2 := ( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)(32,37);; s3 := ( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)(12,27)(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)(41,47);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2); s1 := Sym(47)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47); s2 := Sym(47)!( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)(32,37); s3 := Sym(47)!( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)(12,27)(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)(41,47); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;