            Tutorial for !Stellate


There are three Tutorials:

  1. Instructions for beginners - shows how to make the 3D view plot from the
     stored command data

  2. Instructions for making your own selections from the stellation diagram
     to make your own version of a polyhedron from the stored instructions;
     the second section shows how to select star faces and selecting faces
     from more than one component
 
  3. Instructions for making a new polyhedron by selecting your face types to
     make stellation diagram(s) and a new polyhedron 

If you want to understand the details of how !Stellate stores polyhedra and
their stellations look at the file Reference.Intro.   

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            Tutorial (1) Plotting a stored polyhedron,
      viewing it in several ways and saving the view as a Draw file.

You might find it helpful to turn on the Acorn interactive help before
following these instructions.

  1. Double click on the icon in the filer window to load the !Stellate icon
    on to the icon bar.

  2. Click MENU over the icon to see the menu and select the item Name.
    This opens the Stored solid window with the number of stored polyhedra
    in its title bar, and a list of icons labelled with the names of polyhedra.

  3. Click on the name of one you know, such as the cube.

  4. This opens the Parameters window which has information about the 
selected polyhedron, which is explained in Tutorial 3. For now, click on the
lower right icon Plot Solid if you just want to see the 3D view at once
and skip to section 6. Click on Auto-Select to see the intermediate stage.
Click on Change to create a new polyhedron as described in Tutorial 3.

  5. This opens another window containing a stellation diagram with a
central cyan square (see page 6 of the paper manual for an explanation of
what this is, or look in  Tutorials.Pictures.Page6). The control
panel to the left is loosely connected to this window, it has several
buttons and icons, click on the Plot Solid icon almost at the bottom.

  6. Another window appears showing a 3D view of your chosen polyhedron 
drawn in a single shaded colour. 

Click MENU over the icon on the iconbar and choose 'Description' to open
the Description window listing:
     the name of the polyhedron in the 3D window
     the count of faces, vertices and edges
     the name of its dual
     the Wenninger number (if any).

The default 'Choices' file does not show this window; it appears with the 3D
window until you deselect 'Description' from the menu.
 
   Try using the cursor keys to rotate the 3D view of your polyhedron,
(!Help tells you which keys to use or you can turn on the Acorn interactive
help). Alternatively you can click over any of the top 3 icons in the
adjoining tools pane to rotate the solid.

Also try clicking SELECT in the 3D window. Click on a vertex to see its
number listed in a small window to the lower right with title Face Data.
Click over a face for information about that face. 

There are 4 lines in the window giving the number of the:
  component   ( see list in the Draw file Pictures.Component )
  plane       ( the plane of the polyhedron component)
  face        ( the face number of the face in the stellation diagram )
  Sym/rot     ( the number of the face made by rotational symmetry )

A cube is made from one face, the central square in the stellation diagram.  
To make the cube, this face has been duplicated and rotated as defined by
the angles in the data file Components.  Rotate the cube until you have
seen all the 6 planes. The meaning of the lines in the stellation diagram
should become clearer when you draw a polyhedron with more kinds of polygons
for faces. (Later you may want to look at the Draw files:
TryThese.Answer6a,b,c which show stellation diagrams with faces colour
coded to show which faces they make in the 3D stellation to the right. )
 
7. Now explore what you can do by clicking MENU over this window.

Display 
 - allows you to change the way you look at the 3D solid (the block of 9
   icons in the tools pane also do this while the 3 below them let you add
   perspective, shade and change the light position).
  Since the cube is a simple solid you may find it hard to understand the
different display types. 

   Repeat steps 1 to 6 above but this time select the polyhedron shown on 
page 7 of the manual, the Great Dodecahemidodecahedron (Wenninger #107) and
try looking at the different display types, some of which are in the
Draw file: Tutorials.Pictures.Page7.  

You use the red/green glasses to see the polyhedron in stereo, it looks
better when continuously rotated, just hold down a rotation key, or hold
down the CTRL key and press a rotation key for continuous rotations until
you click the mouse in that window. It does not work with interactive Help
turned on.

Look at the Plane display (4th icon), all the faces which are in the same
plane have the same colour. 

In the #sides display, polygons with the same number of sides are the same
colour.

The components display shows faces which come from the same component in
the same colour. This polyhedron is made from 2 components; click SELECT
over the two colours to see which faces they are. Then move the 3D view
window away from the stellation diagrams underneath; you see which faces come
from each of the 2 stellation diagrams. Notice that the 2nd diagram has
faces in cyan and dark blue showing whether the front or back of the face is
towards you. !Stellate draws only one side of a face; you have to tell it
which one to draw as seen from outside the polyhedron, the front or the back.

Try looking at the central flower, and clicking with SELECT on each of the
inside petals in turn, starting with the one at lower left, move to the next
one in an anti-clockwise direction and notice that the bottom line Sym/rot
changes. Only the first one is drawn in the stellation diagram, the others
are invented by !Stellate because these components are both dodecahedral
with 5 fold symmetry, so after your draw one, it knows to replicate that one
until there are 5 altogether.  

If you want to see a polyhedron with 3 components follow steps 1 to 6 above
to look at the Great Cubicuboctahedron (Wenninger #77) which has:
  component 1: red triangles,
  component 2: green pentagons,
  component 3: yellow 8 pointed stars.

The only stored solid with 4 components is the Snub Icosidodecadodecahedron
 (Wenninger #112).

A good model to show the Front/Back colouring is the Icosahedron
stellation 11 (Wenninger #36); compare the solid with the colours in the
stellation diagram. This colouring method was used to reproduce the solid
figures in the plates of the 3rd edition of The Fifty-Nine Icosahedra,
(Tarquin).

Rotations 
   - allows you to change the angle of rotations for one press of a key

Save 
   - brings up a Save menu, choose the top item Draw to save the
current view to a Draw file by dragging the icon to a filer window. (The
corresponding Save and Print icons are at the bottom of the tools window.)


8. It is easier to see the relation between the stellation diagrams and the
faces they make if you look at each diagram in turn and rotate the 3D view
until you can see the faces corresponding to that diagram. The first
component usually has the bigger diagram, the others are shown below at half
size, you change the one shown bigger either by clicking on one of the
lower diagrams or on the button on the control panel. Change the scale by
using the keys < >, clicking on the up/down arrows in the control panel or
by entering a number in the icon. If you get hopelessly lost, click reset.    
         
You should now be able to look at any of the stored polyhedra and save them
as Draw files.

9.How to know what there is to see.

You see an alphabetical list of polyhedron names when you select by Name.
A list in a different order is stored in Tutorials.CrossRef, which has
the polyhedra under several headings such as compounds, non-convex, those
with 5 pointed stars as faces etc. The sprite file
Tutorials.Pictures.AllPoly has diagrams of the stored polyhedra, and
is printed as a single loose A4 page in your paper manual.

Happy exploring!
