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La teoría de Ehrhart mide un politopo P discretamente, contando los puntos enteros dentro de sus dilataciones P, 2P, 3P, ..... En este artículo calculamos la teoría de Ehrhart de cuatro familias de politopos de gran importancia en varias áreas de la matemática: los permutaedros de Coxeter de los grupos clásicos de Coxeter An, Bn, Cn, Dn. Una herramienta central, de interés independiente, es la descripción de la teoría de Ehrhart de una traslación racional de una proyección entera de un cubo.
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Derechos de autor 2020 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales