Table of Contents

## What is a Polyhedron?

Polyhedron – Explanation

A polyhedron is a three-dimensional figure with flat faces and straight edges. The faces are usually polygons, and the edges are usually lines.

## Parts of Polyhedron

- A polyhedron is a solid figure formed by connecting a series of plane faces, called polygons. The polygons that make up a polyhedron are usually triangles, squares, or hexagons, but any shape can be used. The edges of the polygons are called sides, and the points where two or more sides meet are called vertices.
- There are four basic types of polyhedra, based on the number of sides of the polygons that make them up. These are the triangular prism, the square prism, the hexagonal prism, and the tetrahedron.
- A triangular prism has six triangular sides and eight vertices. The triangular sides are all the same size, and the prism has two square bases, one at each end.
- A square prism has eight square sides and 12 vertices. The square sides are all the same size, and the prism has two triangular bases, one at each end.
- A hexagonal prism has 12 hexagonal sides and 18 vertices. The hexagonal sides are all the same size, and the prism has two square bases, one at each end.
- A tetrahedron has four triangular sides and six vertices. The triangular sides are all the same size, and the tetrahedron has three square faces, one at each vertex.

## Types of Polyhedron

There are five main types of polyhedron:

- Tetrahedron: A tetrahedron is a four-sided, three-dimensional object made up of six triangles.
- Hexahedron: A hexahedron is a six-sided, three-dimensional object made up of 12 squares.
- Octahedron: An octahedron is an eight-sided, three-dimensional object made up of 16 triangles.
- Dodecahedron: A dodecahedron is a twelve-sided, three-dimensional object made up of 20 squares.
- Icosahedron: An icosahedron is a twenty-sided, three-dimensional object made up of 30 triangles.

## Counting Polyhedron Faces, Edges, and Vertices

A polyhedron is a 3-dimensional object with flat faces. Each face is a polygon.

There are three types of polyhedron:

- Convex: A polyhedron is convex if every line segment connecting any two points on the surface of the polyhedron lies inside the polyhedron.
- Concave: A polyhedron is concave if at least one line segment connecting any two points on the surface of the polyhedron lies outside the polyhedron.
- Non-convex: A polyhedron is non-convex if it contains at least one concave face.

## Problems on Polyhedron Faces, Edges, and Vertices

1. What is the difference between a face and an edge of a polyhedron?

A face is the flat surface of a polyhedron. An edge is the line where two faces meet.

2. What is the difference between a vertex and an edge of a polyhedron?

A vertex is the point where two or more edges meet. An edge is the line where two faces meet.