Nearly 150 years ago, Lord Kelvin invented the isotropic helicoid. He predicted that the particle starts to rotate as it moves through a still fluid. This is surprising, because unlike a propeller the particle looks the same from different directions. Kelvin even suggested how to make a paper model 
An isotropic helicoid may be made by attaching projecting vanes to the surface of a globe in proper positions; for instance, cutting at 45 degrees each, at the middles of the twelve quadrants of any three great circles dividing the globe into eight quadrantal triangles. By making the globe and the vanes of light paper, a body is obtained rigid enough and light enough to illustrate by its motions through air the motions of an isotropic helicoid through an incompressible liquid.
Since Kelvin's analysis of isotropic helicoids in the inviscid limit, textbooks have discussed isotropic helicoids in viscous flows. Moreover, there is recent interest in how such particles move in turbulent flow. However until recently there were no experiments testing these ideas.
New experiments show no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling (Figure 1). We explained these results by demonstrating that in creeping flow, the chiral coupling of isotropic helicoids made out of non-chiral vanes is due only to hydrodynamic interactions between these vanes and therefore is small. So Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of non-interacting vanes in creeping flow.
Figure 1. Illustration of the point-group symmetries of different isotropic helicoids. From Ref. . The cubes were drawn after Table 7.2 in Mermin & Ashcroft, Solid State Physics.
 Hydrokinetic solutions and observations
Lord Kelvin, Phil. Mag. 42 (1871) 362
 Lord Kelvin's isotropic helicoid
D Collins, RJ Hamati, F Candelier, K Gustavsson, B Mehlig & GA Voth, Phys. Rev. Fluids 6 (2021) 074302