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The fine dissection of nerves and blood vessels in the tarsal tunnel is necessary for clinical operations to provide anatomical information. A total of 60 feet from 30 cadavers were dissected. Two imaginary reference lines that passed through the tip of the medial malleolus were applied. A detailed description of the branch pattern and the corresponding position of the posterior tibial nerve, posterior tibial artery, medial calcaneal nerve and medial calcaneal artery was provided, and the measured data were analyzed. Our results can be summarized as follows. I. A total of 81.67% of the bifurcation points of the posterior tibial nerve, which was divided into the medial and lateral plantar nerves, were located within the tarsal tunnel, not distal to the tarsal tunnel. II. The bifurcation points of the posterior tibial artery were all located in the tarsal tunnel. Almost all of the bifurcation points of the posterior tibial artery were lower than those of the posterior tibial nerve. The bifurcation point of the posterior tibial artery situated distal to the tarsal tunnel was not found. III. The number and the origin of the medial calcaneal nerves and arteries were highly variable.

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A so-called representation (rep) group G is introduced which is formed by all the | G | distinct operators (or matrices) of an abstract group G in a rep space L and which is an m-fold covering group of another abstract group g. G forms a rep of G. The rep group differs from an abstract group in that its elements are not linearly independent and thus the number n of its linearly independent class operators is less than its class number N. A systematic theory is established for the rep group based on Dirac's CSCO (complete set of commuting operators) approach in quantum mechanics. This theory also comprises the rep theory for abstract groups as a special case of m -\. Three kinds of CSCO, the CSCO-I, -II, and -III, are defined which are the analogies of J 2 , (J 2 ,J Z ), and {J 2 ,J Z ,J Z )> respectively, for the rotation group S0 3 , where 7 2 is the component of angular momentum in the intrinsic frame. The primitive characters, the irreducible basis and Clebsch-Gordan coefficients, and the irreducible matrices of the rep group G in any subgroup symmetry adaptation can be found by solving the eigenequations of the CSCO-I, -II, and -III of G, respectively, in appropriate vector spaces. It is shown that the rep group G has only n instead of N inequivalent irreducible representations (irreps), which are just the allowable irreps of the abstract group G in the space L. Therefore, the construction of the irreps of G in L can be replaced by that of G. The labor involved in the construction of the irreps of the rep group G with order | G |. is no more than that for the group g with order | g | -| G | /m, and thus tremendous labor can be saved by working with the rep group G instead of the abstract group G. Based on the rep-group theory, a new approach to the space-group rep theory is proposed, which is distinguished by its simplicity and applicability. Corresponding to each little group G(k)

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