Classifying Solids Using Angle Deficiency
Age 11 to 16
This article takes you through the classification of the Platonic
(regular) and Archimedean (semi-regular) solids, to find all of
them and prove that there are no more.
I found it difficult to make a choice of article for the NRICH
Tenth Anniversary Celebration. I chose this one because it has been
the basis of so many enjoyable sessions that I have had both with
young learners and also with teachers.
With any age group, from 10 upwards, I find the best approach is to
explain the Schlafli code and demonstrate it with an actual
Archimedean solid,and then to give individuals
different codes with the task of making their solid for that code.
According to how much time you have, and how much your group
already know, you can structure the session so that they discover
the Euler Relation and/or the total Angle Deficiency, you can
arrive at a proof that there are only 5 Platonic Solids and you can
fill in the tables for all the Archimedean Solids deducing the
number of each shape of face as described in the article. There are
In the ATE Maths Superweek where the photos were taken we had a
great Holiday Director called Ian Johnston and a very good cook
called Mrs Higgins and the children never knew that these were one
and the same person. Just before lunch on the morning we spent on
this topic Ian (an engineer) joined us and the children, having
decided to test him, excitedly showed him their models "Ian look at
mine, it's a 466" , "Ian mine is a 3434, can you explain that?"
... and so on. It did not take long for Ian (an
engineer) to work it out and the children were
Perhaps your class can make the models out of card and hang them
from the ceiling.