The Construction Parameters:

The Stars shape comes with a few interesting properties. Especially when playing with taper and depth you can get a rich set of different usefull base shapes to start with. In the examples below i have added the basic setting for our Logo and the basic setting for creating plant using alpha textures.
The Construction Parameters:
 U Faces (Default=8):Range[3, …] The number of U Faces directly corresponds to
the number of points in the star (#points = #faces / 2).
Attention: only even numbers of faces give regular star shapes.  V Faces (Default=8): Range[1, …]
 Depth (default=0.6, range= [1,+1]): Defines the sharpness of the points:
 depth:1 collapses the vertices inbetween the points to the zaxis.
 depth:0 yields a double headed cone (all points are vened out).
 depth:1 pulls the vertices inbetween the points far out,
so that now the star shape reverts the inner points and the outer points.
 Taper(default=1): Defines the opening of the poles
 taper:1 top and bottom poles are fully collapsed.
 taper:0 top and bottom poles are fully opened.
 Rotate (default=0): Range [360,360]
Examples
orthogonal planes (for plants and trees)  

U Faces  8  
V Faces  8  
Depth  1.000  
Taper  0  
Rotate  0  
Subdiv. level  2  
If you use this technique, then please also rotate the UVmap by 90 degrees in the UV image editor and use texture type “planar” in the SL texturing options for your object. This will reduce the Alpha sorting problem.
the 5 pointed star (basic shape for our Logos)  

U Faces  10  
V Faces  4  
Depth  0.616  
Taper  1  
Rotate  36  
Subdiv. level  2  
Please note that only even numbers in U face count will create regular stars. And only power of 2 numbers in U and V face count allow for for texturing with tileable textures.