Activity 1: Having Fun with Objects

Submit a photo of the most interesting object you have made (including the types and numbers of pieces that you used to make the object) to to have it included in the Fan Zone section of our gallery. The objects on the right are an example of the wide range of possibilities when building an object.

Your creations are limited only by your imagination!

► Click here to submit your creation now

Activity 2: Platonic Solids

Use the shapes (polygons) in the GeoGenius construction kit to make each of the Platonic solids. The text below is a useful guide.

If all of the sides of a shape are the same length and all of the angles of the shape are the same size then the shape is called regular or regular polygon. There are 6 regular shapes (polygons) in the GeoGenius construction kit- equilateral triangle: square; and regular pentagon; hexagon; octagon and decagon.


Above Left: Regular Pentagon Right: Irregular Pentagon

Platonic solid is the name given to an object that has identical regular shapes (polygons) for all of its faces. These solids are names after the ancient Greek philosopher, Plato.

It can be shown that there are only five possible objects which have the property that all of their faces are made from identical regular polygons.

► Click here to download a pdf of the Platonic and Archimedean Solids

Activity 3: Archimedean Solids

The collection of solids made from regular polygonal sides of two or more types that meet in a uniform pattern around each vertex are called the Archimedean solids. The solids are named after Archimedes who is the first person to have described them. It can be shown that there are exactly 13 possible Archimedean Solids.

Use the shapes (polygons) in the GeoGenius construction kit to make each of the Archimedean solids.


Top L-R: 1. Cuboctahedron 2. (Small) Rhombicuboctahedron 3. Truncated Cube 4. Truncated Icosahedron 5. Truncated Tetrahedron
Middle L-R: 1. Icosidodecahedron 2. Snub Cube 3. Truncated Cuboctahedron 4. (Small) Rhombicosidodecahedron 5. Truncated Octahedron
Bottom: 1. Truncated Icosidodecahedron 2. Snub Dodecahedron 3. Truncated Dodecahedron

► Click here to download a pdf of the Platonic and Archimedean Solids

Activity 4: Prisms, Pyramids & Anti-Prisms

We have names for different families of objects. Below is a guide explaining Prisms, Pyramids and Anti-Prisms. Using this guide, and your GeoGenius construction kit pieces, make as many prisms, pyramids and anti-prisms as you can.

Activity 5: Prism, Pyramid and Anti-Prism Patterns

In order to complete this activity you should be aware of the following vocabulary:

The 2-D shapes (polygons) used to make 3-D objects (polyhedra) are referred to as the faces of the object (polyhedron). The place where two faces of an object meet is called an edge. The place where the edges of an object meet is called a vertex.

► Click here to download this activity

Activity 6: Making Stellated Objects

By extending the edges or faces of an object until they meet again we can create what are called stellated objects – stellated because they look like stars.

Use the pieces in the GeoGenius construction kit to make the objects below.


L-R: 1. Stellated Octahedron 2. Stellated dodecahedron 3. Stellated icosahedron

► Click here to download a pdf of Stellated and Faceted Objects

Activity 7: Making Faceted Objects

By removing solid pieces from a polyhedron it is possible to make what are known as faceted polyhedron.

Use the pieces in the GeoGenius construction kit to make the faceted objects below.


L-R: Faceted Icosahedra and Faceted Cuboctahedra.

► Click here to download a pdf of Stellated and Faceted Objects

Activity 8: Johnson Solids

A Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex.

As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex.

Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of Johnson solids always have 3, 4, 5, 6, 8, or 10 sides.

Use the pieces in the GeoGenius construction kit to make some of the Johnson Solids (or all 92!). Here are 5 examples for you:




L-R: 1.Triaugmented Dodecahedron 2. Gyroelongated Square Bicupola 3. Augmented Truncated Cube
        4. Gyrate Bidiminished Rhombicosidodecahedron 5. Disphenocingulum

► Click here to download a pdf of Johnson Solids

Activity 9: Making Nets of Objects

1. Make nets for and construct a range of different objects.
2. Use the GeoGenius construction kit to explore how many different nets you can use to make a particular shape.

Rather than making an object from individual faces as we do when we use the GeoGenius construction kit, it is also possible to do so by cutting out what is called the net of the object and folding and pasting this together. The GeoGenius construction kit is a powerful tool that can be used to design the nets of objects. To do so simply follow the steps below:

STEP 1:	Make the object that you want to design a net for using the pieces of the GeoGenius construction kit. In the illustration we are making a net for a square-based pyramid.
STEP 2:	Carefully remove elastic bands from the object one by one until you can completely flatten the entire surface of the object. Make sure not to remove so many elastics that the pieces come loose.
STEP 3:	Make a rough sketch of the net of the object.
STEP 4:	Make an accurate drawing of the net on a piece of light cardboard – you might want to use the pieces from the GeoGenius construction kit to trace around but leave off the tabs as you do so.
STEP 5:	Add glue tabs to the net that you have created- put one on every second edge.
STEP 6:	Cut out the net and crease (score) the fold lines of the net.
STEP 7:	Assemble and glue the object that you have made.