3D Rotation Symmetry - Cube and Tetrahedron

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Lesson Objective
In this lesson, we will learn about the rotation symmetry for a cube and  tetrahedron.
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About This Lesson
After familiarizing with the basics on rotational symmetry, we can now examine the rotational symmetry for three dimensional (3D) objects.

In this lesson, we will see examine all the axes of rotational symmetry for a cube and tetrahedron.


cube
tetrahedron











                        CUBE                             TETRAHEDRON

You can proceed by reading the study tips first or watch the math video or try out the practice questions.

Study Tips

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Tip #1
For 3D rotational symmetry, the ideas are basically the same as 2D Rotational symmetry.
 
Looking at the picture, when we rotate the cube 360o about the axis, notice that the cube will fit (i.e. match) itself for 4 times.

When this happens, the axis is called the axis of rotational symmetry of order 4. 
 
cube rotational symmetry
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Tip #2
Note that, the cube has a total of 13 axes of rotational symmetry. You can view them by watching the math video below.

Also, the step-by-step solution shown in the practice question will show you the pictures for these axes.


axes of rotational symmetry for a cube
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Tip #3
As for the tetrahedron, it has a total of 7 axes of rotational symmetry. You can view these axes in the math video below.

Also, the step-by-step solution shown in the practice question will show you all the pictures of these axes.


axes of rotational symmetry for a tetrahedron

Math Video

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Rotation Symmetry for a Cube Video
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Rotation Symmetry for a Tetrahedron Video
 
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Math Videos Transcript

Practice Questions & More

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Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on rotation symmetry or pick your choice of question below.
  1. Question 1 on axis of rotational symmetry for a cube
  2. Question 2 on axis of rotational symmetry for a tetrahedron
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