
        Tutorial (2) Selecting faces on a stored stellation diagram
               and saving the new polyhedron for later viewing
  
 1. Follow steps 1 to 5 of Tutorial (1) to get the stellation diagram of
the dodecahedron on the screen, with its control panel to the left. 

 2. There is a cyan pentagon in the centre with a red circle around it. 
This is the radius of the sphere which is just big enough to contain the
polyhedron itself, sometimes called a circum-radius or ex-radius. 
Click the third icon button in the control panel if you do not want to 
see this circle, which is more useful when you are selecting your own
polyhedron (See Tutorial (3) later). See Draw file ExParams for more
explanation.

3. The diagram can be scaled either by using the keys < >, by clicking on
the up and down arrows inside the box labelled Scale in the control panel
or by typing the size into the white scale icon. The reset icon returns
the diagram to the original size.  When you have the diagram drawn at a 
convenient size you can save it to a Draw file by clicking on Save at the
bottom of the panel. You get the lines in the Draw file which you can see in
the window. You may have to scale it to get all the lines you want to see
into it, or exclude others. 
                           
4. To erase the central pentagon, click ADJUST anywhere within the stellation
diagram.

5. You select a closed polygon from the stellation diagram either by clicking
on lines or points, depending on which icon of the control panel is selected.
You can only switch between the two methods before you have selected
anything.

a)   Using Lines 
This is the default because the lines in the stellation diagram are made by
projecting the faces on to a plane (see Tutorials.Pictures.Page6).
You can either select an area immediately surrounded by lines (just click in
the middle of the area to select it and turn it cyan) or select the lines
around a more complicated area. The method of selecting the lines round an
area is described first because it is more general. 
 Put the cursor on one of the lines surrounding the central pentagon, and
click SELECT. The line should change colour; if it is too fine to see
easily, you can change the thickness of the lines to suit your display (select
Line widths from the icon bar menu). Then move on to the next line round
the pentagon and click on that and continue in this way until you have
selected all the lines surrounding your chosen polygon. The next line you
click on must intersect the previous one and you should not skip any of the
lines on the way round. After you have selected 3 lines the icons Front
and Back will no longer be greyed out, so you can end the selection of a
face, but you can continue to select more lines up to a limit of 12. When
you have selected the five lines round the pentagon, go to step 6 (below).
 If you click SELECT in the middle of an area surrounded by lines it will
turn cyan showing that is is selected as Front. Try this with your
pentagon: first erase the pentagon you have outlined by clicking ADJUST
until all your selections have been erased; then click SELECT in the middle
(but not quite over the black spot) and the pentagon will turn cyan.
If you had wanted to select a Back face in this way you must use the MENU
button rather than the SELECT one (ADJUST is used to erase selected faces.)
Step 6 (below) is not needed if you use this method of selecting areas. If
you select adjacent areas in this way they will be joined to make a single
area (provided they do not include the central area or a star). 


Important rules on selecting faces:

i)   the lines (or points) must be selected in order, clockwise 
     (or anti-clockwise) round the face (otherwise you will get the warning
     message Lines are measured in the wrong order etc.);
ii)  the symmetry of the diagram is shown in brackets after its name in the
     window title; do not select faces that will overlap when the symmetrical
     faces are automatically generated (otherwise you will get the warning
     message New face overlaps itself etc.);
iii) do not select faces that overlap previous faces (otherwise you will get
     the warning message New face overlaps a previous face etc.); 
iv)  the spot in the middle of the diagram is to help in making star faces:
     using Lines (or Points) click on the central point first, then select
     the three (or more) lines which are needed to make a point of a star,
     starting with the chord which is closest to the centre, then going round
     the other lines needed to make one arm of the star; this is replicated
     for you by the symmetry of the component. 5-pointed stars have 5-fold 
     symmetry and need three lines to make one point of the star; eight (ten) 
     pointed stars have four (five)-fold symmetry and need two points of the 
     star for each section requiring the central spot and five (or six)
     lines to create them.
     The Draw file Pictures.Non-convex shows four types.

b)  Using Points to select your faces.
This works in exactly the same way except that now you must click over the
intersection of two or more lines, and you see a small circle over the
points you have selected. Click ADJUST to erase the last point selected. You
can not select areas while in the Points mode.

6. !Stellate only draws one side of a face; you have to tell it which side
you want to see after you have selected all the points you want for that face.
Click on the icon labelled Front in the control panel, this will colour the 
selected face(s) cyan in the stellation diagram. Most faces are Front; this 
means that an observer looking from the outside of the polyhedron sees that 
side of the face. Some non-convex polyhedra have faces which you want to see
from the other side. (Look at the small cubicuboctahedron, W69, for example
and also display it in 3D using the Front/Back colouring option.)
Click on Back for these faces, which will then be coloured blue in the 
stellation diagram. You can change a previously selected face from Front
to Back by clicking over it with MENU or from Back to Front with
SELECT. Ignore the Split icon for now; it is only needed for very complex
polyhedra and is explained in Reference.Splits. The Reflect icon is only
used with dual models and is explained in Reference.Duals.

7. When you have selected all the faces click on Plot Solid in the control
panel to see your polyhedron; in this case it is a dodecahedron.

8. Return to the stellation diagram. This window stays open after you click
on the Plot Solid icon in the control panel to see the 3D view. However,
if you have drawn the 3D view by clicking on the Plot Solid icon in the
Parameters window, the stellation window does not open. To open it, close
the 3D view window by clicking with ADJUST over its close icon.
 
To make the 1st stellation erase the central pentagon, and click SELECT in
one of the small triangles coloured cyan in Tutorials.Pictures.Page6 in
the diagram labelled 1st stellation. Five triangles will be coloured cyan
since the diagram is 5-fold symmetric (the number in the () in the window
title is the symmetry of the diagram).

You can save the stellation diagram as a Draw File by clicking on the Save
icon in  the control panel to open the usual Save window with an icon you
drag to the filer window where you want to save the diagram. Click Plot
Solid again to see the polyhedron.

9. Now make the 2nd and 3rd stellations in the same way. The 3rd is much
bigger so you will need to reduce the size of the stellation diagram to see
the larger triangles.

10. Your new polyhedron can be saved in 3 ways, to see what they are, click
MENU over the 3D window, move down to the Save item and across to see the
3 options (alternatively use the icons at the bottom of the tools window):

  Draw       saves a Draw file of the current 3D view; unlike saving the
               stellation diagrams, here the whole polyhedron is
               saved, regardless of how much is visible in the window.
               A description of the polyhedron is also saved in the draw file
               if you have Description selected in the main menu.
  PolyData   saves a PolyData file, with suitable format for later display
               in the drawing program !PolyDraw (see later).
  Line/instr saves the 3 lines of data needed to display the polyhedron
               again in !Stellate, without having to remember which lines
               you selected in the Stellation diagram. The default filename
               is NewLine. If you save to a file which already has some
               polyhedron drawing instructions, you will be allowed to
               overwrite the file or append the new instructions.
  
You save them in the usual way by dragging the Save icon, which appears
in a small window when you move the cursor to the right, to a filer window.

Polydata files are used with applications !Polydraw and !PolyNet
(see the file Products on your distribution disc)

NewLine files can be appended to the file Resources.StellaList
using the editor if you always want to have the drawing instructions for the
new polyhedron available. When you drop a NewLine file on to the icon
bar it will replace the current list of polyhedra. To get back the original
set, drop the file Resources.Stellalist on to the icon on the iconbar
again. If you want to edit your Stellalist file it is a good idea to copy
the original to a backup file before editing, so that if something goes
wrong with your editing you will still be able to use the original file.

11. Using Dual and Reflect
  All convex solids have a dual; try displaying the snub cube and selecting
item dual from the 3D view Menu. This is not stored; it is calculated by
!Stellate when requested. You can give the dual another name by moving the
cursor to the right over the item 'Dual' in the menu before you click on
the item. Notice that the Description window changes as well as the 3D view.
clicking on 'dual' again will bring back your original polyhedron. The
middle icon on the 6th row in the tools pane also selects the dual.
 
  Some solids have an orientation to them (see enantiomorph in
Docs.Reference.Glossary) if you want to see the right handed form of the
snub cube click on the last item in the 3D view window Reflect.
(Look at Tutorials.Pictures.Snubduals to see how the views differ.)

       Part 2: selecting faces from more complicated solids

1. Star faces are constructed using the central point in the stellation
diagram as the origin for making one petal of the star and using the
symmetry to reproduce the others. The draw file Pictures.Non-convex shows
how this is done.

2. Polyhedra with more than one component.
  The simplest examples combine cubic and octahedral components. First
select the cube in !Stellate and see that its stellation diagram has two
pairs of lines at 45 forming a square in the middle. Next look at the
diagram for an octahedron; this has two pairs of lines at 30 and one pair
at 90 with one of each making the central triangle. Now look at the diagram
for the cuboctahedron (W11). You will see that there are actually two
diagrams, a big one as before and a smaller one underneath. The big one is
the octahedral diagram and contains the same six solid lines as the
diagram for the octahedron but now there are also six dotted lines, three of
them forming a smaller equilateral triangle in the middle.
  The Draw file Pictures.Ex2Comp shows the octahedron and the cube at the
top left in the orientation for making the octahedral stellation diagram.
The octahedron sits on the plane (in the same way as the dodecahedron did in
the simple example above) but the cube pushes a vertex through the plane.
There are three faces at the vertex of a cube so these faces will make three
lines on the stellation diagram. The lines made by the cube in the
octahedral diagram are shown dotted (just to distinguish them from those
made by the octahedron) and the small triangle they make is a triangular
face of the cuboctahedron. In Pictures.Ex2Comp you can see this in the
diagram below where the vertices of the cream coloured cube have been cut
off to form the orange triangles by the octahedral diagram.
   Now look at the pictures on the right. Here the cube sits on the plane
and the octahedron pushes a vertex through to form the square faces on the
cubic stellation diagram. Go back to the cuboctahedron stellation diagram in
!Stellate and click on Component2 in the panel on the left. This makes
the cubic (or hexahedral) diagram at the top where you can see the four
lines from the original cube (shown dotted) and the four lines from the
octahedron vertex (shown solid) in between. (There are four more lines from
the other four faces of the octahedron a bit outside the plot - make it
smaller to see them by clicking on the scaling icons and then Reset).
   Select the square face of the cuboctahedron by clicking Select inside
it. Go back to Component1 and select the dotted triangle (formed by the
cube's faces) similarly. Now you can Plot Solid to see the cuboctahedron.
   You can make it have the same colours as used in Pictures.Ex2Comp.
Select Display/Component/Unshaded from Menu over the 3D window. This makes
a green and red cuboctahedron. Click Adjust over a green square and change
its colour to cream; click Adjust over a red triangle and change its
colour to orange. Now you could rotate the solid with the arrow keys and
save it as a Draw file just as was done to make the pictures in
Pictures.Ex2Comp.
   Now try the other Archimedean solids with two components which all have
the central areas of both their components selected as Front. Notice that
the lines on both diagrams formed by the first component are solid and those
formed by the second component are dotted.
   Finally, try the Archimedean solids with three components. The lines
formed by the third component are shown dashed to distinguish them from the
other two.

You should now be able to select your own faces from any of the stored
stellation diagrams and make new polyhedra of your own, which you can save
to see again later.

Tutorial 3 explains how to create a new polyhedron from your own choice of
components using more than one component. 