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In this paper, we propose for the first time the application of ambipolar CNTFETs with in-field controllable polarities to design regular fabrics with static logic. We exploit the high expressive power provided by complementary static logic built with ambipolar CNTFETs to design compact and efficient configurable gates. After evaluating a polarity-aware logic design for the configurable gates, we selected a number of gates with an And-Or-Inverter structure and produced a first comparison with existent medium-grained logic blocks, like the Actel ACT1 and 4-input LUTs [1]. Preliminary evaluation of our gates indicates improvements of around 47% over the ACT1 and of about 18× with respect to 4-input LUTs in terms of area×normalized delay.