The shadows of the 6-cube
Three projections of the hexeract
Change projection and tap a hexagram to follow it across the three shadows of the cube.
The hypercube of 6 dimensions does not fit on a screen: all we can see are its shadows. Here are three, and all three contain the same 64 vertices and the same 192 threads coloured by line. The chosen hexagram lights up, with its 6 neighbours, in the three projections at once: three silhouettes of a single object.
each line is a direction of the plane 30 degrees apart; the outer polygon has exactly 12 vertices (the Petrie polygon of the 6-cube)
the upper trigram chooses the corner of the large cube and the lower one the corner of the small cube; 96 edges live inside the small cubes (lines 1 to 3) and 96 between them (lines 4 to 6)
concentric rings by number of yang lines, from Kun at the centre to Qian at the rim: sizes 1, 6, 15, 20, 15, 6, 1; every edge crosses exactly one level
The first shadow is a relative of the ring in the hypercube experiment; the third is the radial view of the Boolean lattice. Same graph, three geometries.
The three projections of the hexeract (12-vertex Petrie polygon, cube of cubes, and yang levels) preserve the 192 edges of the hypercube.
verificar_sombrasThe types of claim and the full bibliography (APA) are in Foundations.