{'fraction_non_alphanumeric': 0.015580736543909348, 'fraction_numerical': 0.0, 'mean_word_length': 4.566929133858268, '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}}
Geometry of the Copositive Tensor Cone and its Dual

In this paper, we explore some geometric properties of the cones in terms of extreme rays, exposed rays, the exposed face and the maximal face. To this end, we first show that all copositive tensors orthogonal to the generating tensor of the exposed ray in completely positive tensor cone construct a maximal face of the copositive tensor cone, then give a characterization on the maximal face of the copositive tensor cone. Third, we show that each extreme ray of the completely positive tensor cone is an exposed ray in the even order case. Finally, we give a lower bound and an upper bound for the maximal face of the completely positive tensor cone.