no
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The answer depends on how many points there are and how many triplets are non-collinear.
Spheres are the only shapes that have no vertices. A sphere is a three-dimensional shape that is perfectly round, with all points on its surface equidistant from its center. Unlike other three-dimensional shapes such as cubes or pyramids, spheres do not have any corners or vertices where edges meet.
Any number greater or equal to three. You can fit three triangles by joining any vertex to the two opposite vertices. After that, any one triangle can be divided into two by joining any of its vertex to any point on the opposite side.
Any and every triangle has three sides and three angles; that is the defintion. The type of triangle cannot be determined without more information.
Any isosceles triangle which is not also an equilateral triangle. An equilateral triangle would have three.