Overview
- Group
- SmallGroup(1440,5890)
- Rank
- 5
- Schläfli Type
- {2,10,4,6}
- Vertices, edges, …
- 2, 10, 30, 18, 9
- Order of s0s1s2s3s4
- 20
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
5-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46);; s2 := ( 3, 4)( 5, 7)( 8,39)( 9,38)(10,42)(11,41)(12,40)(13,29)(14,28)(15,32)(16,31)(17,30)(18,34)(19,33)(20,37)(21,36)(22,35)(23,24)(25,27)(43,44)(45,47);; s3 := (18,43)(19,44)(20,45)(21,46)(22,47)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42);; s4 := ( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,18)( 9,19)(10,20)(11,21)(12,22)(13,28)(14,29)(15,30)(16,31)(17,32)(33,38)(34,39)(35,40)(36,41)(37,42);; 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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2); s1 := Sym(47)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46); s2 := Sym(47)!( 3, 4)( 5, 7)( 8,39)( 9,38)(10,42)(11,41)(12,40)(13,29)(14,28)(15,32)(16,31)(17,30)(18,34)(19,33)(20,37)(21,36)(22,35)(23,24)(25,27)(43,44)(45,47); s3 := Sym(47)!(18,43)(19,44)(20,45)(21,46)(22,47)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42); s4 := Sym(47)!( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,18)( 9,19)(10,20)(11,21)(12,22)(13,28)(14,29)(15,30)(16,31)(17,32)(33,38)(34,39)(35,40)(36,41)(37,42); poly := sub<Sym(47)|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, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;