Symmetry and Balance
The descriptions of the cities are balanced. At first, Marco Polo's images seem like delicate, pastel paintings with words, but gradually they become darker and soon create a nightmarish panorama of decay and ruins which resembles our modern world. Roughly in the middle of the text he admits that all the cities he has been describing so far are simply different aspects of one city, Venice--which would be the center line of the text's structural symmetry.
Often, Marco Polo also describes the symmetry within a city. For example, Valdrada, a city built over a reflecting lake, appears as two cities: "One erect above the lake, and the other reflected, upside down. Nothing exists or happens in the one Valdrada that the other Valdrada does not repeat." Another example is Andria, which is "built so artfully that its every street follows a planet’s orbit, and the buildings and the places of community life repeat the order of the constellations and the position of the most luminous stars."
Patterns
Invisible Cities is divided into nine chapters, the first and last containing descriptions of 10 cities, while the other chapters contain five each. There are 11 categories of cities with five representative descriptions, so Marco Polo describes 55 cities in total. The structure of nine chapters and interlocked categories resembles Dante's Divine Comedy and its use of the terza rima.
At the same time, the emperor thinks he has discovered Marco Polo's pattern of telling stories, and in his mind he tries to construct a city of his own. He compares the cities to a game of chess and reckons that if he is able to understand the underlying rules, he will be able to understand all his cities and therefore he shall "finally possess [his] empire" even though he has not seen them. The emperor's thinking, his desire to find the underlying rules that govern all his cities, resembles humankind's desire to explain the universe with only a small set of rules, as the search for the Theory of Everything demonstrates.
Language
Similar to the description of the development of cities, Calvino describes the development of language. When Marco Polo meets the emperor for the first time, he does not speak his language and therefore resorts to "gestures, leaps, cries of wonder and of horror, animal barkings or hootings, or with objects he took from his knapsack." However, while the emperor understands what the symbols mean, he is unsure whether he understands the connections between them. Only after Marco Polo has mastered the Tartar language, the national idioms and tribal dialects, the emperor is satisfied.
They soon engage in a philosophical conversation about language and the meaning of words. Describing the city of Hypatia, Marco Polo reports how the "signs form a language, but not the one you think you know." This illustrates the mostly arbitrary relationship between sign and meaning in any language.
