August Mobius discovered his eponymous strip — also found almost contemporaneously by Johann Listing — in 1858, so a pre-1858 Mobius band would be
an interesting object. It turns out there were lots of them.

Mosaic showing Aion and the Zodiac from a Roman villa in Sentinum, ca. 200–250 CE. Now displayed at the Glyptothek Museum in Munich.
Aion, god of eternal time, stands in the celestial belt of the ecliptic decorated with zodiacal signs, with a date palm tree rooted over the horizon and olive tree in the foreground. Date palms and olive trees are ancient, potent symbols of life, endurance, and divinity, deeply rooted in Mediterranean and Middle Eastern cultures. Date palms represent victory, righteousness, and eternal life, while olive trees are globally recognized symbols of peace, wisdom, and strength. Both are regarded as trees of life, or Axis Mundi, that offer nourishment and utility.
Before Aion is the mother-earth Tellus, the Roman Gaia, with four children, the four seasons personified. Crowned with flowers, Spring sits apart from his mother in the bottom left corner & collects flowers for a garland. Summer, wearing a crown made of ears of corn, & Fall, with grapes & other fruit in his hair, sit next to their mother on the left. Wrapped in a long cloak with long sleeves & a hood, Winter lies at the bottom right, holding a willow rod.