Custom post classes for custom post types based on taxonomies Default 'posts' in WordPress have, among other, classes based on their categories and tags. This function adds post classes to custom post types based on taxonomies.

wp-cpt-post-classes.php

<?php
/**
 * Hook
 */
add_filter( 'post_class' , 'zzap_cpt_post_class' );
/**
* Custom post classes for custom post types based on taxonomies
*
* Default 'posts' in WordPress have, among other, classes 
* based on their categories and tags. This function adds 
* post classes to custom post types based on taxonomies. 
* This function is attached to 'post_class' filter hook.
* 
* @param  array $classes  An array of post classes.
* @return array           Returnes filtered post classes
*/
function zzap_cpt_post_class( $classes ) {
	global $post;
	// get post type
	$post_type = get_post_type( get_the_ID() );

	// if post type is not 'post' or 'page' - add 'attachment' if you wish
	if ( ! in_array( $post_type, array( 'post', 'page' ) ) ) : {
		// go to taxonomies array
		$post_type_taxonomies = get_object_taxonomies( $post_type );

		foreach ( $post_type_taxonomies as $taxonomy ) {
			// get all terms for each taxonomy
			$terms = get_the_terms( get_the_ID(), $taxonomy );
			// if we have any term
			if ( ! empty( $terms ) ) {
				// loop through each of them
				foreach ( $terms as $term ) {
					$taxonomy = $term->taxonomy; // this will get taxonomy slug
					$slug     = $term->slug; // this will get term slug
					// finally build our classes in WordPress' default format for categories and tags
					$classes[] = $taxonomy . '-' . $slug;
				}
			}
		}

		return $classes;
	}
	endif;

	return $classes;
}