As the travelers near Digitopolis, they encounter a road sign at an intersection that indicates the city is five miles—or 8,800 yards, or 26,400 feet, or 316,300 inches—away. The road splits into three; they don’t know which to take.

From behind the sign steps a strange creature with a 12-sided head, each side containing a face with a different expression. This Dodecahedron explains, “I have one for smiling, one for laughing, one for crying, one for frowning, one for thinking, one for pouting, and six more besides” (173). He wonders how Milo can do all that with only one face and asks if everyone with one face is named Milo. Milo says people have different names; the Dodecahedron says that, in Digitopolis, every triangle is called a triangle, and circles are simply called circles, and so on. Anything else would be hopelessly confusing.

They ask the Dodecahedron which road to take; he answers with a complicated word problem involving cars, speeds, and road lengths. Milo and Humbug can’t figure it out, and Milo admits that he does poorly at thought problems. Tock figures out that all three roads arrive at the city at the same time.