Exploring 3D space with a computer – Part 4: Scale models
Adrian Oldknow
The Conatainer
The next task is to design the container – which will be based on a dodecahedron.
First we create a `slider’ P on the axis of the bulb. Then we create the plane perpendicular to the axis through P (not shown). The point Q is a `slider’ on the perpendicular to the ground plane through P. The dodecahedron is defined by the vertical plane, the point P and the point Q – these define the plane, centre and vertex of one pentagonal face. Use the CTRL key if the polyhedron appears the `wrong’ side of the plane. The plane can then be masked, and the surface style of the dodecahedron selected as `empty’. The centre O of the dodecahedron is found as the midpoint of two opposite vertices.
The slider R is created on the axis of the bulb OP. We can also construct the pentagonal pyramid with O as vertex. We can `slice’ this with the plane perpendicular to OP through R to obtain the truncated pentagonal pyramid shown. Now we can manipulate P, Q and R to see just what sorts of proportions will be feasible if want these sliced pyramids always to glue together to form a regular solid. The point S has also been added to control the size of a possible circular hole in the large pentagon. You can download the file 
bulb-container.cg3’ and/or manipulate the embedded file below.
We can then reflect and rotate the basic solid - the truncated pentagonal pyramid - to each `cell' in the circumscribing dodecahedron. We can also create the small solid dodecahedron formed by the gap at the centre.
Again you can download this model as ` lamp-shade.cg3' and/or manipulate the embedded 3D object below.
