Monopods (also sciapods, skiapods, skiapodes, Monocoli) are mythological dwarf-like creatures with a single, large foot extending from one thick leg centered in the middle of their body. The name Skiapodes is derived from σκιαποδες - "shadow feet" in Greek, monocoli from μονοκωλοι - 'one legged' in Greek.
References in premodern history
These were described by Pliny the Elder in Naturalis Historia. Pliny describes how travelers have reported their encounters or sights of Monopods in India, and he records their stories. Pliny remarks that they are first mentioned by Ctesias in his book India, a record of the view of Persians of India which only remains in fragments. Pliny describes Monopods as thus (Natural History 7:2):
He [Ctesias] speaks also of another race of men, who are known as Monocoli, who have only one leg, but are able to leap with surprising agility. The same people are also called Sciapodae, because they are in the habit of lying on their backs, during the time of the extreme heat, and protect themselves from the sun by the shade of their feet.
Philostratus mentions Skiapodes in his Life of Apollonius of Tyana, which was cited by Eusebius in his Treatise Against Hierocles. Apollonius of Tyana believes the Skiapodes live in India and Ethiopia, and asks the Indian sage Iarkhas about their existence.
St. Augustine mentions the "Skiopodes" in The City of God, Book 16 in the 8th chapter entitled, "Whether Certain Monstrous Races of Men Are Derived From the Stock of Adam or Noah's Sons." Reference to the legend continued into the Middle Ages, for example with Isidore of Seville in his Etymologiae.
According to Carl A.P. Ruck, the Monopods's cited existence in India refers to the Vedic Aja Ekapad ("Not-born Single-foot"), an epithet for Soma. Since Soma is a botanical deity the single foot would represent the stem of an entheogenic plant or fungus. 
It is possible that the myth derived from a misinterpretation of the practice of Indian yogis (sadhu) who sometimes meditate on one foot.
Modern references and popular culture
Chronicles of Narnia
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In the story, the Duffers, a tribe of monopodal dwarves, inhabit a small island in the far eastern ocean, near the edge of the Narnian world; along with a magician, Coriakin, who was charged with their care. They were originally regular dwarves, with two legs, but were transformed into monopods by Coriakin, as a punishment. The Duffers were so unhappy with their appearance (they said that they had been "uglified") that they made themselves invisible. Lucy Pevensie later made them visible again. They were (re)discovered by explorers from the Narnian ship, the Dawn Treader, which had landed on the island to rest and resupply. The ship was on an expedition to the furthest east; both a voyage of discovery, and a search for a previous Narnian vessel that had been sent on a similar expedition years earlier.
After sorting out certain misunderstandings about Coriakin's role on the island, the visiting Narnians (and three British children from mid-twentieth century Earth: siblings Edmund and Lucy Pevensie and their cousin Eustace Scrubb) taught the Duffers how to navigate on water. By using small oars and jumping on the water lightly, foot-first, the monopodal dwarves were able to row themselves about, each floating on their single, large shoe. Before leaving, the travelers renamed the Duffers "Monopods"; however, the Duffers soon mixed up the name, saying " 'Moneypuds, Pomonods, Poddymons.' " Eventually, they settled on the name "Dufflepuds".
The Dufflepuds looked liked other Narnian dwarves, aside from their monopodality. Their one leg was usually about three feet long, and ended in a large foot, clad in a boat-shaped shoe. When they slept, each dwarf lay on their back with their foot in the air, acting as a kind of umbrella over them; creating a mushroom-like appearance, when viewed from a distance. According to Brian Sibley's book The Land of Narnia, Lewis may have based their appearance on drawings from the Hereford Mappa Mundi.
Skiapods in Baudolino
Sciapod is also part of the Monster in My Pocket series.
There is a South American legend of a monopod woman named 'Patasola'.
Sukiya Podes (a Japanization then re-romanization of Skiapodes) is a character in the Puyo Puyo series.
In the Legend Owain, or the Lady of the Fountain, a massive sciapod is mentioned to have control over the animals and to have outstanding physical strength.
Brazilian modernist Tarsila do Amaral's painting "Abaporu" is said[by whom?] to be a representation of a sciapod.
Tim MacIntosh-Smith briefly refers to edible monopod poets in the preface to 'Yemen - Travels in Dictionary Land'