The more convenient a triangle is to make, the more likely it is the correct shape you have to form to generate part of the complete Vertex picture. Once a line is formed into part of a triangle ...

The vertex shader is used to transform the attributes of vertices (points of a triangle) such as color, texture, position and direction from the original color space to the display space.

Other 3D shapes with least one curved surface are not polyhedra ... of a pyramid are around the polygon base plus the apex vertex. A triangle-based pyramid has four vertices.