Abstract. For any κ ≥ 1aκ-dimensional polyhedron Yκ is constructed such that the Yang index of its deleted product Y ∗ κ equals 2κ. This answers a question of Izydorek and Jaworowski (1995). For any κ ≥ 1a2κ-dimensional closed manifold M with involution is constructed such that index M =2κ, but M canbemappedintoaκ-dimensional polyhedron without antipodal coincidence. The deleted product of Y is the space Y ∗ = Y 2 \ ∆, where ∆ is the diagonal of Y 2. There is a natural free involution T (x, y) =(y, x) acting in Y ∗. Our goal is to compute the Yang index of the deleted product of some polyhedra (with respect to the involution T). In particular, we answer the question in [3] =2κ. It is of whether there exists a κ-dimensional polyhedron Yκ with index Y ∗ κ shown that the space Yκ =[∆2κ+2] κ has index Y ∗ κ =2κ

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