Once students have created a few prisms, introduce them to the vocabulary
words face, edge, vertex. Give each student a Prisms sheet. Have them count
their prisms’ faces, edges and vertices and record the correct values in the
handout.
As a class, go over the handout and fill in any remaining information. If no one
has made a certain type of prism have the students figure out how many edges,
faces and vertices that figure will have. What patterns do they see in the
information?

How does the number of edges of each base relate to the number of total
edges?

What pattern do you see with the number of faces and edges?

What pattern do you see with the number of edges to the number of
vertices?
Discuss the famous mathematician Leonhard Euler, born in Basel, Switzerland
in 1707. Euler, one of the greatest and most prolific mathematicians of all time,
wrote nearly 900 mathematical papers in his life time (half of them after he was
blinded at the age of 60.) He also developed this formula for polyhedrons:
V + F - E = 2 (V=number of vertices, F=number of faces, E = number of edges.
Have the students use Euler’s formula to verify their answers on the prisms
table. Answers are provided to the teacher on the Prisms Answers sheet. Have
them use Euler’s formula to predict the numbers of faces, vertices, and edges of
other prisms (octagonal, nonagonal, and more.)
© 2015 Zeno, All Rights Reserved
-Prisms sheet
-Prisms Answer
sheet
Prisms
Shapes
Number of Faces
Triangular
Prism
Square Prism
(Cube)
Rectangular
Prism
Pentagonal
Prism
Hexagonal
Prism
© 2015 Zeno, All Rights Reserved
Number of Vertices
Number of Edges
Prisms Answers
Shapes
Triangular
Prism
Square Prism
(Cube)
Rectangular
Prism
Pentagonal
Prism
Hexagonal
Prism
Number of Faces
Number of Vertices
Number of Edges
5
6
9
6
8
12
6
8
12
7
10
15
8
12
18
© 2015 Zeno, All Rights Reserved