WASHINGTON — The Supreme Court seems eager to hear a case on the constitutionality of a distinctively American form of punishment: prolonged solitary confinement.

“Years on end of near total isolation exact a terrible price,” Justice Anthony M. Kennedy wrote in a concurrence in a case in June. Justice Stephen G. Breyer echoed the point in a dissent in a case later that month.

An appeal from Virginia materialized almost immediately. Now the justices must weigh whether it has the right features — whether it is, in legal jargon, a good vehicle — to serve as the basis for a major decision on extended solitary confinement, which much of the world considers torture.

On the plus side, the case asks the sort of focused and incremental question that the justices often find attractive: May states automatically put all death row inmates in solitary confinement?