This is a Level 3 Geometry activity from the Figure It Out Series.
A PDF of the student activity is included.
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Students will need to understand the following:
You could begin by making the cube and discussing with students the properties of the cube, especially the polygons that make up the faces and the number of faces, edges, and vertices.
Encourage students to look for polyhedra in everyday shapes found in the environment. You may find the following definitions useful:
An interesting extension and discussion point is Euler’s formula: faces plus vertices minus two will equal the number of edges (F + V – 2 = E). (Euler [1707–1783] was a Swiss mathematician who produced a number of important mathematical works and hundreds of mathematical and scientific memoirs.) If we use an icosahedron as an example of Euler’s formula, 20 + 12 – 2 = 30.
An icosahedron has 30 edges.
A useful question could be: “If I added the number of faces and vertices together, what do I need to do to get the same number of edges as shown in the table? Does Euler’s formula always work?” This formula introduces some algebra and links to the achievement objective: describe in words,
rules for continuing number and spatial sequential patterns, Algebra, level 3.
Investigation
The cube, tetrahedron, octahedron, dodecahedron, and icosahedron are known as Platonic solids. They are named after Plato (428–347 B.C.), who studied each solid intensively. Plato attributed the four main elements in the universe to the platonic solids: fire – tetrahedron, earth – cube, air – octahedron, and water – icosahedron. He also attributed the world to the dodecahedron.
1. Practical activity
2.
Shape | Edges | Faces | Vertices |
Tetrahedron |
6 12 12 30 30 |
4 6 8 12 20 |
4 8 6 20 12 |
Investigation Research on Plato
Printed from https://nzmaths.co.nz/resource/let-s-face-it at 11:40pm on the 25th April 2024