Shape Primitives

Polygons are relatively small and simple 2D primitives used for modeling and rendering. In general, they're no more than figures like triangles, squares, and circles. However, combining into huge polygon meshes, they allow for creating way more complicated models.

Polyhedrons represent three-dimensional shapes — usually pyramids, cubes, and spheres. In general, polyhedrons allow you to create almost any regular or irregular shape by defining a closed surface with vertices and faces.

A Platonic solid is a 3D shape that meets three main requirements:

1. All the faces must be equal and they need to be regular polygons
2. The same number of faces must meet at each vertex
3. The shape must be convex — for example, it can't be something like a star

Only five solids meet the criteria: tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons.

So, not every polyhedron is a Platonic solid. A polyhedron is any three-dimensional shape with flat polygonal faces, straight edges, and sharp corners or vertices. Polyhedrons that aren't convex, or constructed by identical polygons, for example, aren't considered Platonic solids.

A cube is a regular hexahedron — hexa means six in Ancient Greek — with equal square faces. The cube is the only regular hexahedron and is one of the five Platonic solids.

We bet you know what a sphere is. We literally see and touch something very similar every day. And yes, we're talking about the planet Earth, which isn't a perfect sphere, but it comes close. In general, a sphere is a three-dimensional object shaped like a ball. Every point on the sphere's surface is at the same distance from its center.

A tetrahedron is an object with 4 triangle-looking faces. Imagine if Egyptian pyramids had a triangular base instead of the square ones — that's what a tetrahedron looks like. As we mentioned, a tetrahedron could be one of the Platonic solids, if all of its faces are regular (or equal, which is the same).

An icosahedron is a polyhedron that has 20 faces, 30 edges, and 12 vertices. In the realm of 3D design, it's a geometric shape that you might encounter for various purposes. Here's a breakdown of its key uses:

• Complex structures: It serves as a building block for more complex 3D structures.
• Low-poly modeling: For creating simplistic yet visually striking models, designers often use shapes like the icosahedron.
• Gaming: Due to its symmetry and simple structure, it's often used in game design for dice or other symmetrical objects.
• User interface elements: Sometimes you'll find icosahedrons in interactive designs where the shape's various faces can represent different options or outcomes.

Since octa means eight in Ancient Greek, an octahedron is an object with 8 faces, which, again, is triangle-looking. The shape looks like two pyramids joined at their bases. Fun fact: most of the diamond crystals are octahedral.

A dodecahedron is an object with 12 faces. In turn, a regular dodecahedron — one of the Platonic solids, you're right — has regular pentagons as faces. And every pentagon, as you probably remember, consists of 5 edges. This shape isn't very common in real life.

Rectangular pyramids have a rectangular base and 4 triangular faces. Many ancient civilizations like Egyptians and Mayans built such pyramids. A rectangular base allows the distribution of the weight of the top of the pyramid over an ever-widening area, making the structure incredibly stable.

We're not going to talk about cylinder hats, which are associated with classical Western fashion. And we're not going to discuss all cylinders that you need to fire on, according to the idiom. But what we would like to mention is a cylinder as a three-dimensional object. A cylinder has the same flat base and top with one curved side.

It's hard to imagine a children's party — especially birthdays, obviously — without birthday hats. But what do they look like? Right, like a cone. A cone has a circle at one end, a point — the apex or vertex — on the other, and a curved side between them.

We all carry cone cells, or cones, in our eyes.

Rings, donuts, lifebuoys, bagels — these are just a few examples of a torus in our life. A torus is a three-dimensional object created by revolving a small circle around a line made by a bigger circle. Unlike many other objects that we were talking about, a torus has no edges.

A torus knot is a knot that lies on the surface of an unknotted torus. This knot winds around a circle in the interior of a torus a particular number of times. It also curves around the axis of the torus of rotational symmetry — a property a shape has when it looks the same after rotation by a partial turn.