Platonic Figures

Platonic solids are regular polyhedra that were made by Plato, a greek mathematician from Athens. There are five platonic figures, all unique and different (Boswell, Lee, and Larson).

The first is a cube, which is a very well-known shape.  It’s six faces are squares and if you flattened the shape into a net, it would look like a cross. It has 6 faces, 8 vertices, and 12 edges (Boswell, Lee, and Larson).

The second is a tetrahedron. When I showed a picture of a tetrahedron to my friends, they insisted it was a triangular pyramid. Both names are correct, but tetrahedron sounds cooler. Its net looks like a Triforce, or, if you don’t know what that is, it looks like an equilateral triangle split by its mid segments. It has 4 faces, 4 vertices, and 6 edges (Boswell, Lee, and Larson).

The third is an octahedron. This shape is popular for making dice, because is has 8 congruent sides. The faces are equilateral triangles. The net is a bit too complicated to explain, but you can see the picture of the net that I made! :D It has 8 faces, 6 vertices, and 12 edges.

The fourth is an icosahedron, which is like an octahedron on steroids. It has 20 equilateral triangle faces. This shape is amazing for making dice for Dungeons and Dragons or Magic the Gathering….*sigh* It has 20 faces, 12 vertices, and 30 edges (Boswell, Lee, and Larson)

The fifth one is a dodecahedron, which was a pain to make a net for. Its net is made of 12 pentagonal faces. It has 12 faces, 20 vertices, and 30 edges.

Surface area of a Tetrahedron:

So, to find the surface area, we first need to find the area of one of the faces. In some cases you could have the height of the triangle, but if you don't have that, and only have the length of the sides, you could use the area formula above.

A= 1/4 (square root of 3) s^2

A= 1/4 (square root of 3) (2) ^2

A= 1/4 (square root of 3) (4)

A= (1) (square root of 3)

A= (square root of 3)

Now you just multiply this number by the number of faces. In this case, its 4.

SA= 4(square root of 3) inches squared

Now, let's try finding the surface area of a cube.

A=bh

A= (1) (1)

A= 1

Now multiply it by the number of sides, 6.

SA= 6(1)

SA= 6 square inches