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32 Edges Reveal a 4D Cube
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32 Edges Reveal a 4D Cube

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Can one continuous line reveal a four-dimensional cube?

A tesseract has 16 vertices and 32 edges. Each vertex is one of the 16 sign combinations (±1, ±1, ±1, ±1), and two vertices are connected when exactly one coordinate changes sign. The line traces every edge once before a 4D rotation and perspective projection turn the structure into the cube-within-a-cube form shown here. The complete construction appears in the video.

Artismathic turns equations into visual art—one function at a time.

Music: 'Taking Chances' by The Soundings

#MathArt #Tesseract #4DGeometry

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V=(±1,±1,±1,±1)V = {(±1, ±1, ±1, ±1)}E=(vi,vj):exactlyonesignchangesE = {(vᵢ, vⱼ): exactly one sign changes}q(u)=R4[(1−u)vi+uvj]q(u) = R₄[(1 − u)vᵢ + uvⱼ]P(q)=7.2(q1,q2,q3)/(3.25−q4)P(q) = 7.2(q₁, q₂, q₃)/(3.25 − q₄)0≤u≤1⋅all32edgesonce0 ≤ u ≤ 1 · all 32 edges once
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