Transum Software

Faces, Edges and Vertices

Show your ability to recognise the attributes of three dimensional solid shapes with this self marking quiz.

Level 1 Level 2 Level 3 Description Help More 3D Shapes

This is level 3; Applying Euler's Formula. You can earn a trophy if you get at least seven questions correct.

One of Euler's Formulas applies to any polyhedron that does not intersect itself. If the number of faces is F, the number of vertices is V and the number of edges is E then:

F + V - E = 2

How many edges does a solid shape have if it has six faces and eight vertices? Correct Wrong
How many edges does a solid shape have if it has four faces and four vertices? Correct Wrong
How many faces does a solid shape have if it has six vertices and twelve edges? Correct Wrong
How many faces does a solid shape have if it has thirty edges and twenty vertices? Correct Wrong
How many vertices does a solid shape have if it has twenty faces and thirty edges? Correct Wrong
A polyhedron has five more edges than vertices. How many faces does it have? Correct Wrong
A polyhedron has twelve more edges than faces. How many vertices does it have? Correct Wrong
How many faces does the polyhedron have that has the same number of faces as vertices and two more edges than vertices? Correct Wrong
A polyhedron has 58 edges and it has the same number of faces as vertices. How many faces does it have? Correct Wrong
A polyhedron has 48 edges and it has the same number of faces as vertices. How many faces does it have? Correct Wrong

This is Faces, Edges and Vertices level 3. You can also try:
Level 1 Level 2

The animated diagrams are licensed by Kjell André under the Creative Commons Attribution-Share Alike 3.0 Unported license.


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Featured Activity

Strategy Games

Strategy Games

We have collected together lots of strategy games for you to enjoy. Many of them have mathematical principles involved in their design so would make a good activity for a Mathematics lesson.


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:


Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2018 WWW.TRANSUM.ORG

Description of Levels



Level 1 - Count the number of faces, edges and vertices.

Level 2 - Discovering Euler's Formula.

Level 3 - Applying Euler's Formula.

Nets of 3D Shapes


Sorry, This animation requires Flash.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.