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Also known as n-cube, n-eract, octachoron
In geometry, a hypercube is an n-dimensional analogue of a square (two-dimensional|) and a cube (Three-dimensional|); the special case for Four-dimensional space| is known as a tesseract. It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to \sqrt{n}.
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在几何学中,超方形(英語:Hypercube),又称立方形、正测形(Measure Polytope)是指正方形和立方体的n维类比(对于正方形,n=2,对于立方体,n=3)。它是一类封閉的、紧致的、凸的图形,它们的1维骨架是由一群在其所在空间对准每个维度整齐排列的等长的线段组成的,其中相对的线段互相平行,而相交于一点的线段则互相正交。在n维空间中单位超方形(棱长为1)的对角线长等于. 一个n维的超方形又被叫做n-超方形。“正测形”(Measure Polytope)也是一个常用的名字,尤其是在H.S.M.考克斯特的文章中(这个词最先是由Elte,1912发明的),但它现在已被“超方形”和“立方形”代替了。(而然在日本,由“Measure Polytope”翻译过来的“正测形”仍在使用) 超方形是一种特殊的(也被叫做正交形)。 一个单位超方形是棱长为1个单位长度的超方形。通常,一个角(或叫顶点)是2n个在Rn中的各坐标值等于0或1的点的超方形被特指为在这个坐标系下的基本单位超方形。
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Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).