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Star colloids are rigid particles with long and slender arms connected to a central core. We show numerically that the colloid shapes control the rheology of their suspensions. In particular, colloids with curved arms and hooks can entangle with neighbor particles and form large clusters that can sustain high stresses. When a large cluster permeates the whole system the viscosity increases many fold. Contrary to the case of spherical colloids we observe that these effects are very strong even at moderate volumes fraction over a wide range of Péclet numbers.

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