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This work is licensed under a Creative Commons Attribution 4.0 International License. ; Topological crystalline insulators are a type of topological insulators whose topological surface states are protected by a crystal symmetry, thus the surface gap can be tuned by applying strain or an electric field. In this paper we predict by means of ab initio calculations a new phase of Bi which is a topological crystalline insulator characterized by a mirror Chern number nM = −2, but not a Z2 strong topological insulator. This system presents an exceptional property: at the (001) surface its Dirac cones are pinned at the surface high-symmetry points. As a consequence they are also protected by time-reversal symmetry and can survive against weak disorder even if in-plane mirror symmetry is broken at the surface. Taking advantage of this dual protection, we present a strategy to tune the band-gap based on a topological phase transition unique to this system. Since the spin-texture of these topological surface states reduces the back-scattering in carrier transport, this effective band-engineering is expected to be suitable for electronic and optoelectronic devices with reduced dissipation. ; We acknowledge the computational support from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. MGV and EVC acknowledge partial support from the Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), the Spanish Ministerio de Economía e Innovación (Grant No. FIS2010-19609-C02-01 and FIS2013-48286-C2-1-P), the FEDER funding, Saint Petersburg State University (Project No. 15.61.202.2015) and the Tomsk State University Competitiveness Improvement Program. FM thanks 'Financiamiento Basal para Centros Cientificos y Tecnologicos de Excelencia FB 0807' and Fondecyt grant 1150806. AHR acknowledge the support of DMREF-NSF 1434897 and the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research under contract 54075-ND10. This work was supported by SPP 1666 of the Deutsche Forschungsgemeinschaft (DFG). ; Peer Reviewed