Prisms, Pyramids, and Platonic Solids
Prisms
Prisms are polyhedrons with two parallelogram-shaped lateral faces connecting two congruent polygonal bases. They can be found as triangular, rectangular, or pentagonal prisms, among other shapes. Prisms are frequently found in commonplace items like buildings and packaging.
- Triangular Prism: It has triangular bases and three rectangular lateral faces( faces of a polyhedron that are not based).
- Rectangular Prism: It has rectangular bases and four rectangular lateral faces.
- Pentagonal Prism: It has pentagonal bases and five rectangular lateral faces.
Pyramids
Pyramids are polyhedrons with triangular faces that converge at a single vertex known as the apex along with a polygonal base. Tetrahedrons, square pyramids, and pentagonal pyramids are a few examples of pyramid shapes. Pyramids have been used in construction, including the Egyptian pyramids, and are frequently related to past civilizations.
- Tetrahedron: It has three triangle faces that converge at the top.
- Square Pyramid: Four triangular faces that converge at the top make and has a square base.
- Pentagonal Pyramid: This structure has five triangular faces that converge into a pentagonal base.
Platonic Solids
Five convex polyhedrons with identical regular polygonal faces and equal angles make up a distinctive category called “Platonic solids.” They consist of the cube, octahedron, dodecahedron, and icosahedron, as well as the tetrahedron.
Mathematicians and philosophers have been attracted to the unique symmetry characteristics of platonic solids for centuries. They are related to the philosophical elements of Plato and are seen as depicted geometric forms.
Detailed examples of platonic solids are discussed under “Examples of Polyhedron”.
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Polyhedron | Meaning, Shapes, Formula, and Examples
A polyhedron is a three-dimensional shape with flat polygonal faces, straight edges, and sharp vertices. Examples include cubes, prisms, and pyramids. However, shapes such as cones and spheres do not qualify as polyhedrons because they lack polygonal faces. It can have any polygon such as a triangle, pentagon, hexagon, etc. as faces as well and it satisfies Euler’s formula, which will be discussed later in the article.
In mathematics, polyhedrons have received a great deal of attention and are used in various fields such as Physics, computer graphics, crystallography, architecture, and other disciplines. In this article, we will discuss all the concepts related to polyhedrons including polyhedron definition, polyhedron shape, types of polyhedrons, their faces, edges, vertices, and real-life examples of polyhedrons.
Table of Content
- What is a Polyhedron?
- Polyhedron Meaning
- Polyhedron Shape
- Polyhedron Examples
- Real-Life Examples of Polyhedrons
- Polyhedrons Faces, Edges and Vertices
- Prisms, Pyramids, and Platonic Solids
- Prisms
- Pyramids
- Platonic Solids
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- Polyhedron Types
- Regular Polyhedron
- Irregular Polyhedron
- Convex Polyhedron
- Concave Polyhedron
- Some Other Types of Polyhedrons
- Polyhedral Dice
- Polyhedron Formula
- Euler’s formula for Polyhedron
- Practice Problems on Polyhedrons