The topology is shown in the image, there are 12 faces, 20 nodes and 30 edges. I started with node 1 as the pole, and compute the resistance at all other nodes with 1000 Ω resistors along the edges. The same MATLAB program found 5 possible solutions:
Category 1: drain at nodes 2,3 and 4: 633 1/3 Ω
Category 2: drain at nodes 5,6,7,8,9 and 10: 900 Ω
Category 3: drain at nodes 11,13,14,17,19: 1066 2/3 Ω
Category 4: drain at nodes 12,15,18: 1133 1/3 Ω
Category 5: drain at node 20: 1166 2/3 Ω
I guess the code is sufficiently debugged now, the answer agree with what I found on the internet.
If you can do the cube, then you can also do the icosaeder, the topology is as follows:
Enter the topology in the program that I used for the cube, and of course, the Kirchhoff conditions are automatically generated. With 1000 Ω resistors I found:
Configuration 1: From node 1 to node 12 : 500 Ω
Configuration 2: From node 1 to node 6 : 366 2/3 Ω
Configuration 3: From node 1 to node 7 : 466 2/3 Ω
For configuration 1 the current solution shows zero ampere between nodes 2-3, 3-4, 4-5, 5-6 and 6-2 and also between nodes 7-8, 8-9, 9-10, 10-11 and 11-7. For the other configurations this is not the case.
Are there volunteers to solder the “resistor icosaeder” and verify the answers?
For any amateur band above 20m this is the easiest solution in the field, a 5 meter whip antenna with a magnetic suction mount on the trunk of your car, it results in a SWR of 1.6 and you can tune it to anything above 20m by simply shortening the whip. MFJ makes these, the MFJ 1979 is the whip and the MFJ 336T is their magnetic suction mount. I haven’t tried this on the roof yet since I’m slightly worried about the thickness and the lack of anything that provides more stiffness. After posting these images on facebook the first reaction of my cousin was, are you now also carrying foreign license plate numbers? I rest my case about opinions in our country.
WSPR on LF and MF at respectively 136 kHz and 474 kHz. I listened with my loop antenna and was able to pick up a few stations, MF (11 stations seen) was easier than LF (4 stations seen). On LF there are two strong digital signals near the narrow band that we are interested in. One problem to solve is the frequency stability of the SDR. The airspy LO is somewhat temperature compensated, but it tends to drift. but there is a possibility to connect it to a frequency reference. I’m not sure how amateurs make an transmit antenna for these frequencies, that could be a challenge.