Chichen Itza

Each of the four faces carries 91 steps, and with the top platform the count reaches 365. At the equinoxes a shadow shaped like a serpent runs down the side of the stair.

At 168m this is the largest court of the civilisation, its walls standing 8m high. A quiet voice at one end carries to the other.

A sinkhole sixty metres across from which gold, jade and human remains were recovered as offerings. The water is cloudy, the bottom invisible, and swimming is not allowed.

Windows cut into a round tower were set to follow the movement of Venus. Their directions line up with star positions on particular dates.

Rows of columns fill this section, and a roof once covered them. Each carries a warrior in relief, and no two are quite the same.

Five minutes from the ruins, a circular shaft sixty metres across with a stair cut down into it. Vines hang to the surface and the water runs over forty metres deep.

After dark, projections onto the pyramid tell the Maya history. The ticket is separate and the entrance differs from the daytime one.

Forty minutes away, a town of painted houses around a square. A sinkhole sits inside the town itself and is walked into for a swim.

A quieter site where climbing the pyramid is still permitted. Stucco figures below the summit survived because earth had covered them.

Arriving as the gate opens buys about an hour with few people around. The sellers have not set up yet, so the avenue is clear.

A stepped temple above the Thousand Columns, a reclining Chac Mool with a dish on its belly guarding the top doorway. The two entrance pillars are feathered serpents, heads to the ground. Climbing is barred; admire it from the plaza below.

A long low platform east of the ball court, its four walls carved with rows upon rows of skulls. Scholars believe the heads of sacrificial victims were displayed on stakes here. Each skull's expression differs, which only shows when you step up close.

A square platform on the path between the Kukulcan pyramid and the Sacred Cenote. Stairs climb every face, and the walls bear Venus glyphs and feathered serpents with human heads in their jaws. It is believed to have been a stage for ritual dances.

A large complex in the site's southern part, nicknamed the Nunnery by the Spanish for its many rooms. The east wing's front is one solid mass of Chaac rain-god masks, a style unlike the north plaza buildings. Off the tour-group route, it stays quiet.

A pyramid that looks like a scaled-down Kukulcan. A vertical shaft runs from the top to a natural cave below, where excavators found the bones of several people with offerings, hence the tomb name. You pass it heading for the southern section.

A limestone cave some 6km east of the ruins; when a sealed passage was opened in 1959, Maya incense burners and offerings sat just as they had been left. Visits follow a guide through narrow passages, hot and humid. The floor is slick; trainers help.

Two cave cenotes next to each other in the village of Dzitnup near Valladolid. Shafts of sunlight fall through holes in the roof, and tree roots dangle down to the water. One ticket covers both, and the light falls straightest around noon when the sun is high.

A cenote where a stone path runs into the middle of a round cave and ends on a small circular platform over the water. When light from the roof hole strikes that platform, the queue for photos grows long. The water is clear but the swimming area is small.

A town painted yellow from end to end, centred on the 16th-century San Antonio monastery built atop a Maya pyramid. Its atrium ranks with the biggest in the Americas. Behind the town, the Kinich Kak Moo pyramid is one of Yucatan's largest.

A village cenote about 15 minutes west of the ruins, run by a cooperative of local women. It is a wide open well with the sky above, and wooden steps descend to the pool. The restaurant at the entrance is theirs too.