![]() ![]() This paper presents novel advances in the development of the interaction platform to generate 3D models using both constructive solid geometry and artificial intelligence. This formula is still considered one of the massive milestones in the field of geometry as it altered the entire way of thinking with regard to solids and space.I-nteract is a cyber-physical system that enables real-time interaction with both virtual and real artifacts to design 3D models for additive manufacturing by leveraging mixed-reality technologies. This formula has been acting as a pillar for several findings made by said professionals.Įuler’s formula for polyhedra is a must-know for all students of mathematics. ConclusionĮuler’s formula has been widely used and appreciated by professionals concerned with topology, an extensive branch of geometry that specialises in properties of solid objects preserved even under strenuous conditions and deformations like excessive stretching, pressure, twisting, bending, etc. ![]() However, though quite significant, its only disadvantage is that it applies only to platonic solids or solids that possess defined straight edges and are closed. With recent developments and progress in mathematics, several proofs have been submitted with respect to the formula. It can prove to be helpful in several complex calculations that one might encounter upon future progression into the subject. = 2 which is the statement given by the theorem.īased on the above explanation, it can be understood that this formula can also be useful in finding out the number of either one of the three properties involved when the other two are provided. Here is the calculation with the substituted values of F, V, and E.įocusing only on the left-hand side of the equation, To apply Euler’s formula, which states, F V – E = 2 for the above values, To facilitate a better understanding of the above concept, here is an example where Euler’s formula is applied to deduct the relationship between the vertices, faces, and edges of a simple cuboid.Īs per common knowledge, a cuboid has the following: This formula, however, is confined for usage only with closed solids that possess definite faces and clear cut edges.
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