Technote: Icosahedron Edge Calculation:
Geodesic geometry is rather interesting and occasionally quite challenging. I have recently been involved in a project to explore construction options for a structure based on an Icosahedron form. Although the basic geometry was created using Inventor I was curious about the underlying mathematical formulae pertaining to this type of geometry. I also like to be able to verify key dimensions in the 3d model by separate calculation.
One site I would recommend for calculating this stuff is Rechneronline which provides various options for calculating based on known criteria, an example of which I have shown below.
The formula provided are comprehensive but lacking specifically the formula I was looking for to calculate the edge length for a given radius. The fourth formula in the list does include the value (a) which is the Edge Length and therefore can be transposed to determine the value we need.
Here I have rewritten the fourth formula with the value (a) shown as (L) for clarity.
To determine the value (L) the transposed formula would be thus:
This is a small snippet of information that I hope may be of some use for anyone interested in Geodesic geometry. I should note that the 4 is a multiplication of the sum of the parenthesis and not a power to 4 superscript.
To use this in Inventor the formula can be entered as follows in the parameter dialogue box as a user parameter called “EdgeL”:
The resulting Model value verifies the “d112” dimension from the 3d model.