Overview
- Group
- SmallGroup(640,21131)
- Rank
- 5
- Schläfli Type
- {2,40,2,2}
- Vertices, edges, …
- 2, 40, 40, 2, 2
- 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
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42);; s2 := ( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)(16,22)(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42);; s3 := (43,44);; s4 := (45,46);; 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, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(46)!(1,2); s1 := Sym(46)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42); s2 := Sym(46)!( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)(16,22)(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42); s3 := Sym(46)!(43,44); s4 := Sym(46)!(45,46); poly := sub<Sym(46)|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, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;