Visualising Solid Shapes - Plane Figures and Solid Shapes (Faces, Edges, Vertices)

Two-dimensional (2D) shapes, also known as plane figures, have only two dimensions like length and breadth. Examples include triangles, rectangles, and circles. In contrast, three-dimensional (3D) shapes, or solid shapes, have length, breadth, and height (or depth), such as cubes, cylinders, and spheres.

Solid shapes are composed of three main elements: Faces, Edges, and Vertices. A face is the flat surface of a solid. An edge is the line segment where two faces meet. A vertex is the point (corner) where three or more edges meet. For instance, a cube has $6$ faces, $12$ edges, and $8$ vertices.

A net is a 2D skeleton or pattern that can be folded to form a 3D solid. It represents the 'unfolded' version of a solid. For example, the net of a cube consists of $6$ squares arranged such that they can be folded along the edges to enclose a cubic volume.

3D shapes can be represented on 2D paper using two main techniques: Oblique Sketches and Isometric Sketches. Oblique sketches use squared paper where the front face is drawn to size but other faces are not proportional. Isometric sketches are drawn on dot paper (isometric dots) where lengths are kept proportional to allow accurate representation of the object's dimensions.

Visualising 3D objects involves looking at them from different perspectives, namely the Front View, Side View, and Top View. For example, a cylinder looks like a rectangle from the front or side, but appears as a circle from the top view.

A cross-section is the 2D shape obtained when a 3D solid is 'sliced' by a plane. The shape of the cross-section depends on the direction of the cut. For example, a horizontal slice of a cone results in a circle, while a vertical slice through the vertex results in a triangle.

Shadows provide a way to visualize 3D objects in 2D. When a light source projects onto a solid, it casts a shadow on a surface. The shadow's shape is a 2D representation; for instance, a cube can cast a square shadow, while a cylinder can cast either a rectangular or circular shadow depending on the light's direction.