Overview
- Group
- SmallGroup(1600,8115)
- Rank
- 5
- Schläfli Type
- {2,5,2,40}
- Vertices, edges, …
- 2, 5, 5, 40, 40
- Order of s0s1s2s3s4
- 40
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (4,5)(6,7);; s2 := (3,4)(5,6);; s3 := ( 9,10)(11,12)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)(24,30)(25,29)(32,37)(33,36)(34,39)(35,38)(40,41)(42,45)(43,44)(46,47);; s4 := ( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,32)(18,34)(20,25)(21,27)(23,29)(26,40)(28,42)(30,35)(31,36)(33,38)(37,46)(39,43)(41,44)(45,47);; 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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(1,2); s1 := Sym(47)!(4,5)(6,7); s2 := Sym(47)!(3,4)(5,6); s3 := Sym(47)!( 9,10)(11,12)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)(24,30)(25,29)(32,37)(33,36)(34,39)(35,38)(40,41)(42,45)(43,44)(46,47); s4 := Sym(47)!( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,32)(18,34)(20,25)(21,27)(23,29)(26,40)(28,42)(30,35)(31,36)(33,38)(37,46)(39,43)(41,44)(45,47); 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, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;