Editing Ehrhart polynomial (section)

==Interpretation of coefficients==
If {{math|''P''}} is [[closed set|closed]] (i.e. the boundary faces belong to {{math|''P''}}), some of the coefficients of {{math|''L''(''P'', ''t'')}} have an easy interpretation:

* the leading coefficient, <math>L_d(P)</math>, is equal to the {{math|''d''}}-dimensional [[volume]] of {{math|''P''}}, divided by {{math|''d''(''L'')}} (see [[lattice (group)|lattice]] for an explanation of the content or covolume {{math|''d''(''L'')}} of a lattice);

* the second coefficient, <math>L_{d-1}(P)</math>, can be computed as follows: the lattice {{math|''L''}} induces a lattice {{math|''L<sub>F</sub>''}} on any face {{math|''F''}} of {{math|''P''}}; take the {{math|(''d'' − 1)}}-dimensional volume of {{math|''F''}}, divide by {{math|2''d''(''L<sub>F</sub>'')}}, and add those numbers for all faces of {{math|''P''}};

* the constant coefficient, <math>L_0(P)</math>, is the [[Euler characteristic]] of {{math|''P''}}. When {{math|''P''}} is a closed [[convex polytope]], <math>L_0(P)=1.</math>