Drag the solid to turn it

Drawing Palette Background Stroke 0.5 Show the dual inside Mark the vertices Turn on its own

There are exactly five, and there is no sixth: at three faces per vertex the angles still leave room to fold, and past a point they add up to a full turn and the corner falls flat. Euclid closes the Elements with the proof.

Every face, edge, dual, measurement, and net on this site is computed from the vertex coordinates alone - nothing is drawn by hand, so the numbers and the picture cannot disagree.

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