Platonic Solids

Platonic Solids

Did you know that the five platonic solids that exist in nature represent the five elements i.e. earth, wind, fire, water, and the universe? Sadly, you won't get an environment-loving superhero coming out of the combination of these five elements.

Check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.

But platonic solids are fun to learn, and in this chapter, we will know more about them. In this lesson, you will know more about platonic sold geometry, understand the platonic solid names, and solve some interactive problems.

Lesson Plan


Define Platonic Solids

A platonic solid is a regular, convex polyhedron.

They are named after the ancient Greek philosopher Plato.

A platonic solid has equal and identical faces.

The same number of faces meet at each vertex.

There are 5 regular platonic solids:

1. Tetrahedron

2. Cube

3. Octahedron

4. Dodecahedron

5. Icosahedron

platonic solids


What are the Properties of Platonic Solids?

Following are the properties of a platonic solid:

  1. All the faces are regular, convex polyhedron
  2. Faces of platonic solid do not intersect except at their edges.
  3. The same number of faces meet at each vertex.


What are the 5 Platonic Solids?

There are 5 regular platonic solids:

1.Tetrahedron: 

Tetrahedron
It is made up of equilateral triangles

platonic solid, tetrahedron

Faces 4
Edges 6
Vertices 4
Faces meeting at each vertex 3

2.Cube

Cube
It is made up of square faces

platonic solid, cube

Faces 6
Edges 12
Vertices 8
Faces meeting at each vertex 3

3. Octahedron

Octahedron
It is made up of equilateral triangles

platonic solid, octahedron

Faces 8
Edges 12
Vertices 6
Faces meeting at each vertex 4

4. Dodecahedron

 Dodecahedron
It is made up of regular pentagons

platonic solid, dodecahedron

Faces 12
Edges 30
Vertices 20
Faces meeting at each vertex 3

5. Icosahedron

Icosahedron
It is made up of equilateral triangles

platonic solid, icosahedron

Faces 20
Edges 30
Vertices 12
Faces meeting at each vertex 5

 

 
Thinking out of the box
Think Tank
  • Can you figure out how to make all the platonic solids out of the following 2D diagrams?

platonic solids, icosahedron, dodecahedron, cube

 

 
important notes to remember
Important Notes
  • An icosahedron is a platonic solid with the maximum number of faces (i.e. 20).
  • An icosahedron and dodecahedron have the same number of edges, i.e., 30.

Solved Examples 

Example 1

 

 

Alan wants to know the total number of faces on the dodecahedron. Can you help him figure out?

platonic solid, dodecahedron

Solution

The dodecahedron has 12 regular pentagon faces.

\(\therefore 12 \)
Example 2

 

 

Rita was given the following information about a platonic solid that it has 3 faces meeting at vertices and has 4 vertices. Can you find out which platonic solid is this?

Solution

Out of all platonic solids, only the tetrahedron has 4 vertices. 

platonic solid, tetrahedron

Hence, the given platonic solid is:

\(\therefore\) Tetrahedron
Example 3

 

 

Demi wants to know the name of the platonic solid shown below. Can you name the platonic solid for her?

platonic solid

Solution 
The given solid has 20 triangular faces and 5 triangles are intersecting at each vertex, which is a property of an icosahedron.

Hence the given solid is-

\(\therefore\) An Icosahedron
Example 4

 

 

Walter was given a task to complete the following table for platonic solids. Can you help him in completing this table?

Shape Name At each vertex
tetrahedron ______ ______ triangles meet.
icosahedron ______ ______ triangles meet.
dodecahedron ______ ______ pentagons meet.

Solution

Shape Name At each vertex
tetrahedron Tetrahedron 3 triangles meet.
icosahedron Icosahedron 5 triangles meet.
dodecahedron Dodecahedron 3 pentagons meet.
Example 5

 

 

Wendy wants to know the number of faces, vertices, and edges do a dodecahedron has?

platonic solid, dodecahedron

Solution

A dodecahedron has:

\(\therefore\) 12 faces, 30 edges, and 20 vertices

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 
 

Let's summarize

The mini-lesson targeted the fascinating concept of platonic solids. The math journey around platonic solids starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. What do the 5 platonic solids represent?                  

The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe.

2.  How many sides platonic solids have?                 

1.Tetrahedron has 4 sides.

2. Cube has 6 sides.

3. Octahedron has 8 sides.

4. Dodecahedron has 12 sides.

5. Icosahedron has 20 sides.

3. Is octahedron a platonic solid?

Octahedron is a regular platonic solid of 8 equilateral sides. So, yes octahedron is a platonic solid.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus