    Tutorial (3) Making a new polyhedron from more than one component

1. Click MENU over the icon on the icon bar and choose the item Own Solid

2. This opens the Own solid window with on the left a box headed
face type showing the possible polygons which !Stellate can use as a face
of the polyhedron, and on the right a box with the allowed number of faces.
There is just a heading in the box at the lower left marked  Selections to
start with; your choice is listed there later.

3. Click on your chosen face type, for example a triangle; its name now
appears in the Selections box, and a lot of the icons in the box on the
right number of faces are greyed out because their numbers of faces cannot
be used to make a uniform polyhedron. (For details of which numbers of faces 
are allowed read Tutorials.Intro or look at the Draw files Component and
Faces in subdirectory Docs.Reference.)

4. Click on your chosen number of faces (try 8) to write the number of faces
and component type into the Selections Box

5. Repeat steps 3. and 4. for the next component. Click the Delete icon to
erase the last selection. A maximum of four components is allowed.
For your second one select squares and 12 (rhombic).
This should give you two components in your Selections box
   No  Type        Component
    8  Triangles   Octa
   12  Squares     Rhombidodeca

6. When you have selected all the components you want this time, click on
the OK icon. If polyhedra with these particular components are stored
already, you will see the Choose window, where you can either select one
of the stored ones or create your own new one.  If there are no stored ones
with  these components, the Choose window does not open, and you see the
Parameters window immediately.

   There are no stored solids for our example of 8 triangles and 12 squares.

7. In the Parameters window you must enter the name of your new polyhedron,
followed by <Return>. (Draw file 'Pictures.ExParams' explains the different
parts of this window.) You also enter the radius of the components in the
two icons for each component at the right; the first is the distance from
the centre to a sphere drawn inside the component (in-radius), the other the
distance to the outside (ex-radius). The ex-radius must be at least as big
as the polygon radius shown in the component parameters box on the left.
Press <RETURN> after entering either number when the other will be
calculated and displayed. Alternatively you can enter a radius for the whole
solid in the icon at the top right; the computer will then calculate the
radii of the components.

   For our example enter the name Rhombitruncated octahedron and in-radii
of 0.9 for the Octa component and 1.0 for the Rhombidodeca component
(pressing <return> after each entry). After you do this the polyhedron
radius may change, since it must be at least as big as the largest of the
components ex-radii. If you enter a number in the 'polyhedron' radius, it
will be copied into all the other ex-radii.

   When you have entered all of these click on User-select.

   Then a large stellation diagram opens with a spot in the centre to mark
the origin where you start if you are asking for a star of some sort. There
is a smaller diagram for the other component below the main one. The lines 
are drawn solid or dotted, depending on whether they are made by the first
or second component. (See Draw file Tutorials.Pictures.Ex2Comp for more
explanations)

8. Now select the central polygon on the 1st diagram, a triangle, using the
instructions given in Tutorial2. Draw file Pictures.OwnEx1 shows it
shaded; make this a front one. Click on the lower small diagram to bring
it to the  top, (or click on the icon labelled Component 2 in the control
panel) and select the central polygon (irregular hexagon) again, making it
front too. Then click on Plot solid to see your polyhedron. 

9. Ask to Display it using Unshaded Component colours so that you can see
more easily which faces in the 3D view were made by the faces in each
stellation diagram. By default, the faces from the first component are red,
from the second green (the third would be yellow and the fourth cyan).

10. Try exploring what happens as you change the radii of the two
components; you make larger triangular faces by using a smaller radius for
the triangular component. Faces are drawn at the in-radius distance from
the centre of the polyhedron. If your polyhedron has two components, they
should each be drawn at about the same size so that they intersect one
another. If either is very much larger than the other you will see only that
one. If your radii are very different from each other, you would either see
apparently disconnected faces which do not rotate correctly, or faces which
are not correctly coloured and change as they rotate. The program tries to
check that the faces make a closed polyhedron; if it thinks they are not
connected, another window appears with a warning  message.  Click on 'OK'
in this window and the 3D view is plotted, and points are drawn on the
stellation diagram in which the program thinks there is an  unconnected
edge. This may not be the stellation diagram you worked on last; the program
will draw the diagram with the problem in the main diagram place.

Remember that !Stellate shows only one side of a face (normally the
front and you do not see the back), so that disconnected faces will appear
to vanish when you might expect to see their backs.   

11. Put the two radii back as they were for step 7. and try making the 1st
stellation of your new polyhedron. Try selecting the polygons which are the
next ones away from the centre, as shown in Draw file Pictures.OwnEx1. You
will get the warning that the solid is not closed. Click OK. This makes the
3D solid shown in the centre with 4 blank triangles, the colour of the 
background. At the same time a Diagnostics window opens; a pictorial
explanation of this window is shown in Pictures.Diagnostic.

Click on the only entry in this window which shows that there is a line in
component 2 which ought to be connected to the edge of a face in component 1.
The line is 0.4525 units long and is indicated by red discs in the component
2 diagram; it is a solid line which means that it ought to be connected to a
face of component 1. Correspondingly, the edge of the face in component 1 is
indicated by stars and the edge is dotted which means it should be joined to
component 2; to find which triangle to select in the second stellation
diagram rotate the solid until it is in the position shown in the centre and
try to see the 4 faces in the stellation diagram in one of the green planes
of the polyhedron. You should then be able to see another triangle in the
stellation diagram which should be selected to make the completed 1st
stellation as shown in the bottom row of the Draw file Pictures.OwnEx1. The
triangle to select in the second diagram has the solid line defined by the
red circles.

Note: !Stellate can only attempt to show where to connect a loose edge if
you are making selections using Lines. Try the exercise above using
Points and you will find that the Diagnostics window shows component 1
only and when selected, only the stars along the disconnected edge in
component 1.

Advice on how to select faces to make a closed surface is given in Tutorial2.

You should now be able to make your own polyhedra. Try looking in the file
TryThese.Activities for a few suggestions to help you know where to start.


Fortran Friends welcomes comments on the program and suggestions for new
features or activities. Please send them to:

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