Exploring 3D space with a computer - Part 2: a set of solids
Adrian Oldknow
Reflection
So that ends our tour of the principal functions in Cabri 3D. Using these we can build a variety of working models. For example we can use Rotation to create a model of a door rotating around one of its edges.
Using Reflection we can create a reflected door, so that two doors appear to open and close together.
Here is a barn with a window and some doors. The window was created by dividing the wall into four rectangles leaving a rectangular hole in the middle. Manipulate the image below or download the Cabri 3D file 
Barn doors.cg3. Drag the point X to open and close the doors.
*If you look at the Cabri 3D toolbar you will there are three icons at the right-hand end we have not yet explored.
The seventh icon {3} currently shows an equilateral triangle, and the menu gives a selection of the common regular polygons. The eighth icon currently shows a tetrahedron and the menu gives a selection of common solid shapes - including irregular ones. The ninth icon currently shows a regular tetrahedron and the menu gives a selection of the five regular polyhedra. First we will use the seventh and eighth icons to construct a model of a pencil! This will start with a regular hexagon in the ground plane, which will be used as the basis of a hexagonal prism, on which we shall erect a hexagonal pyramid.
The regular hexagon is constructed in the ground plane with A as centre and B as a vertex. Translations by the vector CD are used to show the stages in the construction. Perpendiculars to the ground plane are drawn through A' and B'.
The point E is taken on the perpendicular through B' and used to define the vector B'E . The base hexagon is translated by B'E to give the top hexagon. The point F is taken on the perpendicular through A' . Using the Prism tool from the eighth icon we create the hexagonal prism using the base hexagon and the vector B'E .
