k[[CurlyPhi]_] := {Cos[[CurlyPhi]] Sin[[Pi]/10 - 1/20 [Pi] Sin[4 [CurlyPhi]]],Sin[[CurlyPhi]] Sin[[Pi]/10 - 1/20 [Pi] Sin[4 [CurlyPhi]]],Cos[[Pi]/10 - 1/20 [Pi] Sin[4 [CurlyPhi]]]}

ParametricRegion[k[[CurlyPhi]], {{[CurlyPhi], 0, 2 Pi}}]
DiscretizeRegion[%]
(* DiscretizeRegion did not find any sample points *)