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Here is the octonion multiplication table drawn on a Möbius strip.
Each red triangle represents a quaternionic triplet.
A right-handed rotation around the triangle follows the multiplication identities.
So the triangle \( e_1, e_2, e_3 \) represents the identities \( e_1 \cdot e_2 = e_3 \), \(e_2 \cdot e_3 = e_1\), and \(e_3 \cdot e_1 = e_2\).

The vertices match up on either side of the Möbius strip.
On alternating sides are triangles skewed in opposing directions.