Siena’s 13th-century Gothic cathedral, with its striped tower, is dedicated to the Virgin Mary and covered with art. The richly ornamented facade bristles with ornamentation: Its striking mosaics framed by patriarchs and prophets, saints, and gargoyles.

Grand as Siena’s cathedral is, it’s actually the unfinished rump of a failed vision. After nearby Florence began building its huge cathedral, proud Siena — not about to be outdone by its rival — planned to build an even bigger church…in fact the biggest church in all Christendom.

But Siena was so hilly, there wasn’t enough flat ground to support such a enormous church. What to do? Build the church oversized anyway, and prop up the overhanging edge by building the Baptistery underneath.

The cathedral we see today was intended only to be a transept, or wing, off the envisioned nave, or main part of the church. These towering marble arches hint at the immensity of the vision. But the arches were as far as Siena got before construction problems and a devastating plague scuttled the project.

I’m standing atop what would have been the front of that church. Had it been completed, this square would have been not a parking lot, but the nave itself.

It’s fun to imagine that if Siena’s grandiose plans had succeeded, I’d be looking straight down the nave of that massive church toward the altar.

The resulting church is still impressive. It’s richly decorated from top to bottom. Peering down from above are 172 heads. They represent the popes who reigned from the time of St. Peter to the 12th century.

The exquisite marble floor is paved with Bible scenes, intricate patterns, and allegories. This one features Siena as a she-wolf at the center of the Italian universe, orbited by such lesser lights as Rome, Florence, and Pisa.

The greatest artists of their day helped decorate Siena’s cathedral. In this side chapel, St. John the Baptist, carved by Donatello, wears his iconic rags. And high above, playful cherubs dangle their feet.

This memorial to the Sienese pope Pius II features a statue of St. Paul carved by Michelangelo himself. And in another chapel, you’ll see why Lorenzo Bernini is considered the greatest Baroque sculptor. His St. Catherine is in spiritual ecstasy. And St. Jerome caresses the crucifix like a violinist lost in heavenly music.

A highlight is the church’s Piccolomini Library: Brilliantly frescoed, it captures the exuberance and optimistic spirit of the 1400s, an age of humanism when the Renaissance was born. The frescoes look nearly as vivid now as the day they were finished, over 500 years ago. They celebrate the life of one of Siena’s hometown boys — who became Pope Pius II. Each of the scenes is framed with an arch, as if opening a window into the real world.