                Things to try with !Stellate

If you cannot understand how to use the program just with !Help and the
Acorn interactive help, you may find it useful to look in the 3 tutorials in
Tutorials for more detailed instructions, or in Reference.Intro for an
explanation of how !Stellate makes polyhedra. Draw files of all the Platonic
solids are in the sub-directory Tutorials.Pictures.

If you get stuck, you can get help from the file Answers. 

1. a)Look at polyhedra with one component which you have seen before, such
as the Platonic solids using different display forms, using the Plot Solid
icon from the parameters window. 
   b)Try looking at them again, but this time use the Auto-Select
icon so that you can see the stellation diagrams used to make the polyhedra.
   c)Try using the User-Select icon and select your own face on the
stellation diagram and draw the 3 D view.
   d)Try changing parameters such as the radii and see whether it makes any
difference to the view displayed.

2. Repeat all 4 stages of step 1 with the Archimedean Solids. These have 2
or 3 components; do their radii have to be about the same size? Does it
matter which is the largest? See if you can find what limits of the radii
can be used to produce a closed polyhedron for these components.

3. Try making all the 1st stellations of the Platonic Solids for yourself and 
make a Draw file showing them all. Do they all have stellations?

4. Try making all the stellations of the dodecahedron for yourself and 
make a Draw file showing them all.

5. Try to make some more stellations of the icosahedron but remember that
the solid must have all its pieces connected.
How many can you make? How many do you think there are altogether?
Why are there so many more for the icosahedron than for the dodecahedron?

6. Try making all the 1st stellations of the Archimedean Solids for yourself
and make a Draw file showing them all.

7. Try making more stellations of the polyhedron shown in
Tutorials.Pictures.OwnEx1 and described in Tutorial3 

8. Look at the cube, and the octahedron and their truncations, which look
as it they were made by slicing off the corners, if you keep slicing you will
turn the cube into an octahedron. These polyhedra have 2 components
the octahedron and the hexahedron (cube). So why are they different polyhedra?
Look carefully at all the windows you see while making these 4 polyhedra and
write down what is different about them.
Can you find any other polyhedra with those 2 components which are
intermediate forms between the cube and the octahedron? Can you make any
more?

9. Try making another Own Choice polyhedron, by making a rhombitruncated 
cube with 6 squares and 12 rhombi squares, internal radius =1

10. Look at the Draw file Tutorials.Pictures.SkelCube which shows you how
to make skeleton polyhedra; try making a Draw file of your own showing a
set of skeletal Platonic solids. Why can you not make skeletal Archimedean
solids? 

11. Try making a Skeletal cube with a solid octahedron inside it. 

12. Look at the compound of 5 tetrahedra; it exists in 2 forms left and right 
handed. Look at the reflected form carefully, while you have the original
stellation diagram on the screen. Then try to make the other form for
yourself. Tutorials.Pictures.SnubDuals shows the 2 forms of the snub cube
which may be helpful.

13. Try to make some compounds for yourself, you might try 2 tetrahedra first
can you make a compound with 3? or with 4?


Fortran Friends will be happy to receive your comments on these activities
and suggestions for others. Send to:

Fortran Friends, P.O.Box 64, Didcot, Oxon, OX11 0TH, UK.
