Seeking 'simple' space with specified homotopy
I am looking for a 'named' space $S$ such that $\pi_1(S) = \mathbb{Z}_2$
and $\pi_n(S) = \star$ (the one-point group) for all $n\geq 2$.
Commentary: I know that the projective plane fits the first requirement
but not the second.
If a 'named' space is lacking, then a construction of such a space would
be a second-best solution.
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