© Steffen Weber, May 1998
Creating a Polyhedron
Click/Drag any point in the Wulff net on the left.
The dots you see moving around are generated by the selected
point group (a set of rotational symmetry operations). Each
dot is the projection of a plane normal (that intersects the
stereographic hemisphere) onto the equator plane (represented by
the Wulff net) A solid dot represents a normal pointing out of
the screen, and an empty circle represents one pointing
away from you. When you release the mouse the corresponding
polyhedron is calculated and displayed in the right window.
When you drag the dots in the Wulff net you can see that the
number of poles (planes) changes as you move to special symmetry
centers. Different numbers of planes means different types of
polyhedra. Therefore you can create several types of
polyhedra in any of the point groups with higher symmetry (eg:
cubic, icosahedral).
Rotations
In order to rotate the right figure around its x-axis use
the right mouse key and the left mouse key to
rotate around the y-and z-axis.
ColorPicker
right mouse button: canvas color
left mouse button: polyhedra color
Pyramids
Please note that for the pyramidal forms I added the basal plane
(00-1), in order to obtain a closed form. This basal plane is NOT
a result of the chosen point group.
Further reading
tutorial on the stereographic projection (explains also the meaning of the Wulff net)
Speed
Be aware that the calculation of general icosahedral polyhedra
with 60 or 120 planes in the point groups 235 & m-3-5
may take quite a while even on fast computers. (but it works!)
Link:Solid Geometry a computer program (© Hope Paul Productions) for generating and printing shapes that can be cut and glued to make 3D bodies.