Six days in Sri Lanka's cultural triangle: two lost capitals and a rock nobody should have built on

Five caves under an overhang at the top of a long flight of steps, filled with more than a hundred and fifty Buddha figures and painted from floor to ceiling with murals that follow the shape of the rock. A king took refuge here in the first century BC and endowed it in thanks; almost every century since has added something. Monkeys work the steps, so carry nothing loose.

The rock a kilometre north of Sigiriya, about the same height, a quarter of the price and a proper clamber over boulders for the last stretch. A reclining Buddha in brick lies in a cave part way up. The summit is the classic view of Sigiriya, best in the last hour of light, and busy at sunrise with everyone who read the same advice.

Sigiriya has almost no restaurants and the guesthouses cook, usually a rice and curry spread ordered a few hours ahead. Say yes; it is the best food you will eat in the triangle.

The first thing inside the gate and the part visitors skip: symmetrical pools, moats and channels laid out in the fifth century, with fountains fed by gravity that still work in the wet season after fifteen hundred years. Walk the western axis for the classic approach to the rock.

King Kassapa built his palace on top of a two hundred metre lava plug in the fifth century, after taking the throne from his father and expecting his brother to come for him. What survives is extraordinary: the cloud maidens painted on a sheltered pocket of cliff, a polished wall covered in visitors' graffiti from a thousand years ago, a staircase rising between the paws of a lion whose head has gone, and a windy summit of brick foundations, cisterns and a throne. Three hours with the descent.

Eat near the entrance or back at the guesthouse, and do nothing at all until half past three. This is the hottest part of the country.

Two national parks north of Sigiriya sharing a corridor of forest, with jeeps leaving for the late afternoon drive. Elephants come down to the reservoir in numbers as the dry season goes on, and in a good year in August you can watch several hundred at once. Insist on a driver who keeps his distance; the scrum of jeeps around a herd is the ugly side of this.

Parakramabahu's palace, which the chronicles claim rose seven storeys and a thousand rooms. Three brick storeys still stand, with the sockets for the floor beams of the ones above and walls three metres thick at the base. The audience hall next door keeps its carved elephants, each one different, and its lion throne.

The quadrangle's centrepiece and the finest building in Polonnaruwa: a circular relic house on a raised terrace, four seated Buddhas facing four stairways, guardstones and moonstones at every threshold, and a ring of stone pillars that once carried a wooden roof. Sit on the terrace edge for ten minutes before moving on.

The stone book, a slab nearly nine metres long dragged here from a quarry a hundred kilometres away and covered in the boasting of King Nissanka Malla. It records what he did, what he owned and what he thought of his rivals, which makes it the most human object on the site.

The hotels along the Parakrama Samudra put tables out facing the water, and the sunset over a reservoir the size of a small sea is worth an early dinner.

The largest stupa in Polonnaruwa, a bare brick dome more than fifty metres high built by Nissanka Malla in imitation of the great ones at Anuradhapura. Walk the terrace clockwise, barefoot, as everyone else does.

A roofless brick image house with walls seventeen metres high, still leaning inwards the way the vaulted roof needed them to. Inside stands a headless Buddha in brick and stucco, and the scale of the doorway tells you what the building was meant to do to whoever walked through it.

The reason people come to Polonnaruwa. Four figures cut in the twelfth century from a single granite wall: a seated Buddha in meditation, a smaller seated figure in a carved cave, a standing figure with folded arms, and a reclining Buddha fourteen metres long entering final nirvana. The stone has bands of colour running through it that the carvers used deliberately. Photography is fine, standing with your back to the figures is not.

The local places on the main road do a vegetable curry buffet for a few hundred rupees at lunchtime, half a dozen dishes and as much rice as you want.

The Sri Maha Bodhi, grown from a cutting of the tree the Buddha sat under, brought here in the third century BC by the nun Sanghamitta and tended by an unbroken line of guardians ever since. It is the oldest planted tree in the world with a written history. Gold railings, prayer flags, families with lotus buds, and a quiet that the rest of the site does not have.

Sixteen hundred stone pillars standing in rows, all that is left of the Brazen Palace, a monastic building of nine storeys roofed in bronze. The pillars are not the original arrangement, and walking into them is still the strangest few minutes at Anuradhapura.

The great white stupa, begun by King Dutugemunu in the second century BC and restored to its full bubble shape in the twentieth. A wall of stone elephants carries the terrace, the dome is floodlit after dark, and this is where the pilgrims are thickest at dusk. Walk clockwise.

Anuradhapura is a working town with little in the way of restaurants; the guesthouses on the edges of it cook properly and you should order before you go out.

A stupa of the third century AD that stood well over a hundred metres high and was, when it was built, one of the tallest structures anywhere on earth. It is being restored, so you see raw brick rather than whitewash, and the scale of the brickwork up close is the point.

The rival monastery, once home to five thousand monks and to the Chinese pilgrim Faxian, who spent two years here in the fifth century and wrote it all down. The site spreads over woodland: a huge stupa, refectories with stone rice troughs, twin bathing pools and the finest moonstone carving in Sri Lanka at the entrance to one of the shrines.

Trains run south to Colombo and north to Jaffna from the station in town, and the road to Kandy takes about three hours. If you are driving to Kandy, Aukana and its standing Buddha cut from living rock is a short detour off the route.