 # Island 5  Goobi: Platonic Solids

What You Should Know:

The challenge is to build and explore the properties of platonic solids. A platonic solid is a "perfect" shape. What makes a perfect shape? Is there such a thing as a perfect shape? In this Learning Launcher, students will explore these questions by building different platonic solids with the Goobi building kit. ## GOOBI: Platonic Solids

How to Use Goobi

The Goobi building set has three parts- balls, bars, and tripods. The bars have magnets on both ends, one positive and one negative. The magnets can be attached to each other or to the nickel-plated steel balls. You can connect up to 12 bars to one ball. The tripods hold in place up to three bars that are used to add strength when building 3D shapes.

Shapes

2D Shapes

Polygons are two-dimensional, or 2D, (flat) shapes. Polygons are made with straight lines that create a closed shape. Regular polygons are polygons where all the sides are of equal length and all the angles are the same.

3D Shapes

Three-dimensional shapes are also called 3D or solids. They do not lay flat. The mathematical name for a 3D shape is polyhedron. Some common 3D shapes include cylinders, cubes, and cones.

The parts of a 3D shape or polyhedron include:

Faces: The polygons that make up the polyhedron

Edges: The lines where faces meet

Vertex or vertices: Points on the polyhedron where the edges meet

Plato's Shapes

Plato was a philosopher and mathematician who lived in ancient Greece. He believed that a "perfect" shape meant that all the angles, edges, and faces should be equal. Plato was interested in how many solid (three-dimensional) shapes existed that were "perfect." These shapes became known as the platonic solids. Plato discovered that there are only five 3D shapes that follow the "perfect rules" of a polyhedron. Closed solids that also have angles and sides that are equal are called polyhedral or platonic solids. The characteristics of a perfect polyhedron or platonic solid are:

• They are made from one type of regular polygon (for example, a cube is made from squares).

• All polygons in the shape are the same size.

• The same number of polygons come together at each point (this means that all of the angles are also equal).

The Archimedean Solids

The second group of regular polyhedra that doesn't totally follow the rules of platonic solids is called the Archimedean solids, and there are thirteen of them. One you might be familiar with is a traditional soccer ball, or truncated icosahedron.

To see examples of more complicated models of this type of symmetry, search for "Uniform Polychora,"  which are 4D versions of your 3D Archimedean solids.