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In this paper we provide new examples of hyperbolic but nonsystolic groups by showing that the triangle groups (2, 4, 5) and (2, 5, 5) are not systolic. Along the way we prove some results about subsets of systolic complexes stable under involutions. ().,-volV) (0123456789().,-volV)doi:10.1007/s00373-020-02209-1 fatcat:nwhrcgmvvndx7k3drpfafyzlfy