Category “same post” retreive and display

# according to your example:
$categories = array ( 'sit', 'leather', 'one person'  );

# get all id's by the category names
foreach ($categories as $category_name) {
$category = get_term_by( 'name', $category_name , 'category' ); 
$ids[] = $category->term_id;
}

# get all posts for the categories
query_posts( 'cat=".join(",',$ids) );

Sorry, I cannot test it right now, this is just a guess till tomorrow.