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In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after Olof Hanner, who introduced them in 1956.〔.〕 ==Construction== The Hanner polytopes are constructed recursively by the following rules:〔.〕 *A line segment is a one-dimensional Hanner polytope *The Cartesian product of every two Hanner polytopes is another Hanner polytope, whose dimension is the sum of the dimensions of the two given polytopes *The dual of a Hanner polytope is another Hanner polytope of the same dimension. They are exactly the polytopes that can be constructed using only these rules: that is, every Hanner polytope can be formed from line segments by a sequence of product and dual operations. Alternatively and equivalently to the polar dual operation, the Hanner polytopes may be constructed by Cartesian products and direct sums, the dual of the Cartesian products. This direct sum operation combines two polytopes by placing them in two linearly independent subspaces of a larger space and then constructing the convex hull of their union.〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hanner polytope」の詳細全文を読む スポンサード リンク
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