Which is the only continent crossed by all lines of longitude?

Antarctica. Every meridian converges at the poles, so a continent containing the South Pole is crossed by all of them - which produces the practical oddity that Antarctica is in every time zone and therefore in none. Research stations simply use the time of their supply country, so neighbouring bases can be hours apart.

It also makes the ordinary rules of navigation break down. At the pole every direction is north, a compass is useless because the magnetic pole is elsewhere and the field points almost straight down, and walking a small circle around the point takes you through every time zone in a couple of minutes.

The territorial claims show the geometry directly: seven countries claim wedges converging on the pole, several of them overlapping, and one sector is claimed by nobody at all - the only substantial piece of land on Earth that no state claims. The Antarctic Treaty of 1959 froze all of it, so the claims exist on paper and mean nothing on the ground, which has held for over sixty years.