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 info@GeoGenius.co.za 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!
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.
PRISM is the name given to an object with identical parallel polygon bases and other faces made of parallelograms.
If the sides of the prism are made using a rectangle the prism is called a rectangular prism – the GeoGenius Construction Kit can be used to make rectangular prisms.
The four rectangular prisms are called (clockwise from top left):
The name of a prism is determined by the name of the shape of the base.
PYRAMID is the name given to an object with a polygonal base whose other faces are all triangles which meet at a point called the apex.
If the apex of the pyramid is above the centre of the base, the pyramid is called a right pyramid – the GeoGenius Construction Kit can be used to make right pyramids.
The name of a pyramid is determined by the name of the shape of the base.
The four right pyramids are called (clockwise top left):
ANTI-PRISM is the name given to an object with identical parallel polygonal bases joined by an alternating band of triangles. The GeoGenius Construction Kit can be used to make anti-prisms.
The name of a prism is determined by the name of the shape of the bases.
The four rectangular anti-prism are called (clockwise from top left):
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.
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 a regular polygon. There are 6 regular shapes (polygons) in the GeoGenius Construction Kit: equilateral triangle; square; regular pentagon; hexagon; octagon and decagon.
Platonic solid is the name given to an object that has identical regular shapes (polygons) for all of its faces. These solids are named 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.
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.
1. Cuboctahedron; 2. Rhombicuboctahedron; 3. Truncated Cube; 4. Truncated Icosahedron; 5. Truncated Tetrahedron; 6. Icosidodecahedron; 7. Snub Cube; 8. Truncated Cuboctahedron; 9. Truncated Icosidodecahedron; 10. Truncated Octahedron; 11. Rhombicosidodecahedron; 12. Snub Dodecahedron; 13. Truncated Dodecahedron.
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:
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.
1. Stellated Octahedron 2. Stellated Dodecahedron 3. Stellated Icosahedron
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.
Faceted Icosahedra and Faceted Cuboctahedra.