Last Updated：2025/11/30

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(geometry) A polytope that is the convex hull of points, two on each Cartesian axis of a Euclidean space, that are equidistant from the origin; an orthoplex.

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cross-polytope

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Source Word

cross-polytope

Noun

Japanese Meaning

（幾何学）ユークリッド空間の各直交座標軸上にある、原点から等距離に位置する2点（各軸ごとに存在）の集合の凸包として定義される多胞体。別名オーソプレックスと呼ばれる。

What is this buttons?

In high-dimensional optimization, researchers often examine the properties of the cross-polytope to understand sparse signal recovery.

Google Translation / DeepL Translation

高次元最適化では、研究者たちはしばしばスパース信号復元を理解するために、各座標軸上に原点から等距離にある点がそれぞれ2つずつある点集合の凸包の性質を調べる。

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Sense（1）

The case p = 1, which is actually important to us, is illustrated in Figure 1.14; we are looking at the intersection of a cross-polytope with the probability simplex.

Google Translation / DeepL Translation

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cross-polytopes

（ plural ）

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cross-polytope

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cross-polytope

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