The Phantom Tollbooth | Study Guide

Norton Juster

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The Phantom Tollbooth | Chapter 14 : The Dodecahedron Leads the Way | Summary



The road divides into three, and a sign gives the distance in miles, rods, yards, feet, inches, and half inches. A strange figure steps from behind the sign and agrees they must decide which road to take. He is the Dodecahedron, and he is constructed from an "assortment of lines and angles" that form a mathematical shape with 12 faces. Each face has a different expression.

The Dodecahedron explains that everything is precise in Digitopolis, and problem-solving is a very important skill. Milo asks him if every road is five miles from the city, and the Dodecahedron replies that they have to be, because they only have one sign. They set off for the "land of numbers," and the Dodecahedron lectures Milo on why "numbers are the most beautiful and valuable things in the world."

The Dodecahedron leads them down into the numbers mine, where they meet the Mathemagician. He is dressed in a flowing robe covered with mathematical equations. They look at the sparkling stones in the mine, and Milo accidentally drops one and it breaks into pieces. The Mathemagician tells Milo not to worry because the broken stones are used for fractions.


The use of equivalent measures to explain the distance to the city brings to mind King Azaz's advisers, who all use different words to say the same thing. Similarly, the Dodecahedron is one character with many faces. Here, the 12 faces of this geometric shape are actual faces—another clever play on words. Feiffer has drawn a clever illustration showing the faces with different expressions on the Dodecahedron's chest.

The Dodecahedron teaches Milo that math and problem-solving are important to know and that math and numbers are as important as words and language. Indeed, numbers are portrayed as being valuable, like precious gems mined from the earth. Despite their value, the Mathemagician notes that it's not a problem when Milo breaks one, since even broken numbers are useful as fractions.

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