People keep asking me questions about the geometry of 'polycone' shapes. The name is my own invention since I don't know of any generic mathematical name for such shapes. I'm referring to three dimensional figures whose base is a regular polygon and whose sides are equilateral triangles all of which meet at a point. A tetrahedron is a three-sided polycone. A pyramid is a four-sided polycone. Frequently stained glass lampshades are frustrums of polycones.
This program will calculate most of the relevant lengths and angles associated with such figures if given:
If I've left out some dimension you need to know, contact me and I'll add it. mklotz@alum.mit.edu.