On the occasion of the fortieth anniversary of the first conference held in Vancouver in Canada in 1978, the 18th International Geometry and Graphics Conference will take place this year, from 3 to 7 August 2018 at the Politecnico di Milano. The International Conference on Geometry and Graphics is a biennial event with a traveling venue, organized under the auspices of the ISGG, the International Society for Geometry and Graphics. As also the logo of the conference tries to summarize, this year the ICGG. will be dedicated to the figures of Leonardo Da Vinci and Giulio Natta. The first will be celebrated as the genius among the greatest in history able to effectively show the enormous power that Geometry and Graphics have had and still play in investigating the relationship between art and science. The second, professor at the Polytechnic of Milan and Nobel Prize in Chemistry in 1963 together with Karl Ziegler, will be remembered as a supporter of the profuse and beauty of Geometry and Graphics in science and technology, especially in relation to the invisible scale of the molecular world. The main themes of the conference will range from research on disciplinary foundations to geometric applications in the real world, especially in the technological field; there will also be in-depth analysis of the didactic aspects of geometry, engineering graphics and industrial design. The conference, therefore, is a meeting place for the presentation and discussion of research and study experiences carried out both in the academic and in the industrial and professional fields.