For N=8 the solution listed on the Wikipedia page is a square antiprism (https://en.m.wikipedia.org/wiki/Square_antiprism https://en.m.wikipedia.org/wiki/Square

For N=8 the solution listed on the Wikipedia page is a square antiprism (https://en.m.wikipedia.org/wiki/Square_antiprism https://en.m.wikipedia.org/wiki/Square_antiprism) which seems intuitively reasonable. But, I don't see anything listed for N=20. Look at the table in S.5 of the article (https://en.m.wikipedia.org/wiki/Thomson_problem#Configurations_of_smallest_known_energy https://en.m.wikipedia.org/wiki/Thomson_problem#Configuratio...) for more links to visualisations in the rightmost column, if one exists.