A triangle, for example, has **three straight sides** and three corners, but a circle has one curved side but no corners. 3D forms A 3D shape is a magnified version of a 2D form. We are studying about 3D forms such as the sphere, cube, cuboid, cylinder, cone, square-based pyramid, and triangular-based pyramid. A cube, like a cuboid, has eight corners. A tetrahedron has four triangles with three sides each, and a pentagon has **five triangles**.

In mathematics, a polygon is any figure formed by joining together a set of points in space. In geometry, the term polygon is used to describe **any closed plane figure** that can be constructed without lifting your pencil from the paper. Thus, a polygon may have any number of sides between two and infinity. A triangle is a polygon with three sides and a quadrilateral is a polygon with four sides. A pentagon, hexagon, heptagon, octagon, nonagon, and decagon are some examples of polygons with more than ten sides.

In mathematics, a surface is a two-dimensional geometric object. Surfaces include planar surfaces, spherical surfaces, cylindrical surfaces, and other shapes. For example, the surface of the earth covers rock inside of it; therefore, the surface of the earth is a type of cover or shell.

3D forms are solid shapes or items with three dimensions (length, width, and height), as opposed to two-dimensional objects with only two dimensions (length and width). Faces, edges, and vertices are also significant words in 3D forms. They have depth, therefore they take up some space. That's why it is important to understand that length, width, and height are all different ways of describing exactly the same thing.

There are several methods used to describe and view 3D shapes. The most common method is to use a pencil and paper to draw free-form diagrams of your object. You can also use software programs to help you design 3D objects. There are many websites with free 3D modeling tools where you can download and try out **different designs** before making your own version. With today's technology, computers are used for designing 3D shapes even before they are made into products. Computer-aided design (CAD) software allows you to create **2D drawings** of objects, which then be transformed into 3D models by using algorithms within the program.

You should know that there are several ways to describe the same shape using **only length**, width, and height. For example, a rectangle is a shape that can be described as length x width. But it can also be described as height x width or length x height. There are also several ways to view a 3D object.

Two-dimensional objects are rotated to form **three-dimensional shapes**. When we rotate a circle, we obtain a sphere; when we rotate a triangle, we get a cone; and when we rotate a rectangle or square, we get a cylinder.

If we rotate a solid about **its own axis**, we produce a new shape that is called an "object" or a "solid". For example, if we rotate a cube around its center point, we get a new shape that is called a "torus" (see figure below). Tori are useful in modeling problems in mechanics, architecture, and other fields related to fluid dynamics. A torus can also be formed by rolling a doughnut into place.

There are two types of solids: those that are continuous and those that are not. A continuous solid has **no gaps** inside it. The human body is an example of a continuous solid. So is wood, although you could break it up with a knife and it would stay together again. Noncontinuous materials such as sand or gravel are used in making pathways or building foundations because they can be easily moved or removed if needed.

Continuous solids can be divided into **two groups** based on how many dimensions they have. Two-dimensional (or flat) solids are those that are thin and rigid. They include sheets of paper, plastic wrap, metal, and glass.

Faces are the flat surfaces of 3D objects. A cube is composed of square faces. Therefore, a cube can be thought of as a special kind of square.

A square will always be made up of **four equal sides**. These four sides can be straight or curved. If they're straight, the square is called "rectangular." If one side is longer than the others, the square is "non-rectangular." Squares can also have two straight sides that are unequal in length. Such squares are also "non-rectangular."

Because rectangles are easier to draw than non-rectangles, that's what teachers usually start with when learning how to draw cubes. But cubes are not only useful for making models; they can be fun to play with too! For example, if you stack several cubes on top of each other, you get a solid object called a "cube stack."

Cubes are important elements in architecture and engineering. They're used to describe **certain properties** of objects that are not necessarily cubes themselves. For example, if something has **a rectangular shape** but isn't actually a rectangle, it's called a "square cube."

Cubes are also useful in puzzles.