![]() Their numbers appear in different papers as for instance in the paper of Plesken. The studied families have been reassembled thanks to the geometric nature of their cell. families numbered XXIII, XXIV, XXV, XXX, XXXII in paper. families numbered XVIII, XXII, XXVI, XXVII in paper. families numbered XII, XVI, XVII, XIX, XX, XXI in paper. families numbered I to XV together with all point groups in paper. families numbered I, II, III, IV, V, VI, VII, XII, XIII, XVI, XVII in paper. the names of the 32 crystal families together with the WPV symbols of their holohedries are listed in paper. The crystal families of five-dimensional space E 5 have been studied in different papers: The crystal families of fourth-dimensional space E 4 have been studied in the paper. Some crystal families of space E 5 can be used to describe di incommensurate structures and quasi crystals. So the study ofĪll crystal families of space E 5 is completed. Mathematical structures and to compare their WPV symbols. TheĪdvantage to classify the point groups in isomorphism classes is to give their Is based on the description of the cell of the holohedry of each crystalįamily and of the results given by the Software established by one of us. Point groups which are classified into isomorphism classes. For each studiedįamily, we explain their name, we describe their cell and we list their Hypercube 5 dim and the (hypercube 4 dim)-al crystal families. The study of three crystal families of space E 5, the (di-iso hexagons)-al, the Point groups of n-dimensional space with n ≤ 6 into different isomorphismĬlasses and we describe some crystal families. In two previous papers, we explained the classification of all crystallographic
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