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Quasicrystals constitute a special category of crystals exhibiting long-range order without periodicity. This strange feature allows them to exhibit rotational symmetries prohibited in regular crystals, such as 5-, 8-, 10- or 12-fold symmetry. Amongst them, icosahedral quasicrystals are the only type that is aperiodic along all 3 dimensions. The present work will focus on Tsai-Type quasicrystals and their approximants, which are the most studied type of icosahedral quasicrystals. We will introduce how they can be generated froma hyperspace perspective, their exotic structure and how it relates to their physical properties. Pressure is a key parameter which can be used to alter the condensed matter properties of a material. By reducing the size of samples and using diamond anvil cells, it is possible to obtain the highest experimentally achievable pressures and collect informations such as magnetization, electrical resistivity or Raman signal. This work will introduce the specialized diamond anvil cells we used to investigate electron transport and magnetization under pressure, explain in details how to circumvent the most common difficulties arising with high pressure setups. and describe how high pressure affects Tsai quasicrystals and approximants in terms of structure and magnetic properties.