Overview
- Group
- SmallGroup(1056,1015)
- Rank
- 4
- Schläfli Type
- {2,44,6}
- Vertices, edges, …
- 2, 44, 132, 6
- Order of s0s1s2s3
- 66
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
11-fold
22-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 5)( 4, 6)( 7,45)( 8,46)( 9,43)(10,44)(11,41)(12,42)(13,39)(14,40)(15,37)(16,38)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30)(25,27)(26,28);; s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,43)(12,45)(13,44)(14,46)(15,39)(16,41)(17,40)(18,42)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(28,29);; s3 := ( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38)(40,42)(44,46);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(46)!(1,2); s1 := Sym(46)!( 3, 5)( 4, 6)( 7,45)( 8,46)( 9,43)(10,44)(11,41)(12,42)(13,39)(14,40)(15,37)(16,38)(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30)(25,27)(26,28); s2 := Sym(46)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,43)(12,45)(13,44)(14,46)(15,39)(16,41)(17,40)(18,42)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(28,29); s3 := Sym(46)!( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38)(40,42)(44,46); poly := sub<Sym(46)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1 >;