Visual icons provide immediate recognition of features on print maps but do not translate well for touch reading by people who are blind or have low vision due to the low fidelity of tactile perception. We explored 3D printed icons as an equivalent to visual icons for tactile maps addressing these problems. We designed over 200 tactile icons (TactIcons) for street and park maps. These were touch tested by blind and sighted people, resulting in a corpus of 33 icons that can be recognised instantly and a further 34 icons that are easily learned. Importantly, this work has informed the creation of detailed guidelines for the design of TactIcons and a practical methodology for touch testing new TactIcons. It is hoped that this work will contribute to the creation of more inclusive, user-friendly tactile maps for people who are blind or have low vision.