© 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.