{'fraction_non_alphanumeric': 0.03189066059225513, 'fraction_numerical': 0.0, 'mean_word_length': 4.365853658536586, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Perfect precise colorings of plane regular tilings

Abstract Let (pq) denote the tessellation of the plane by regular p-gons meeting q at a vertex. In this paper, we consider the problem of coloring (pq) using q colors such that all the q colors appear at every vertex, and that every symmetry (or every direct symmetry) of the tiling (pq) induces a permutation on the set of q colors. Such a coloring is called a perfect precise coloring.