I would 3D-print some Goldberg Polyhedra importing in Sketchup, the coordinates provided on these links:
- 72 faces (2,1) - (coordinates)
- 132 faces (3,1) - (coordinates)
- 192 faces (3,2) - (coordinates)
- 252 faces (5,0) - (coordinates)
I noticed that they have pretty much the same volume, but I need that they have (more or less) the same edge length.
Could you help me understanding how can I calculate the constants (C0, C1, C2 ...) to reach my purpose?
I ran the coordinates through a little perl script to get seom edge length statistics as listed in the following table. If you scale the given polyhedra with "scale factor", the average edge length will become one unit. Notice that the bounding box will grow to an approximate cube of twice the scale factor units side length. $$\begin{matrix}\text{file} & \text{average edge}&\text{std. deviation}&\text{scale factor}\\ \text{DualGeodesicIcosahedron3.txt}&0.265145379472169&0.0124547083541117&3.77151584534764\\ \text{DualGeodesicIcosahedron6.txt}&0.19350606185143&0.0112490031974374&5.16779676270699\\ \text{DualGeodesicIcosahedron8.txt}&0.159756530507094&0.00993562997968005&6.25952502114204\\ \text{DualGeodesicIcosahedron10.txt}&0.139135767498588&0.00896851769224665&7.18722452161808\\ \end{matrix} $$