What you're seeing

The 240 root vectors of the exceptional Lie algebra E₈, projected onto the Coxeter plane — a 2D subspace invariant under a 30-fold rotation of E₈'s symmetry group.

The roots fall onto eight concentric rings, with 30 projected roots on each ring: 8 × 30 = 240.

The highlighted Petrie path follows the outer 30-step Coxeter orbit. Toggle PETRIE in the panel to emphasize it.

The bright glowing roots are an illustrative source highlight chosen by the Studio, not a canonical vertex-by-vertex McKay map.

Click a root to see its 56 Cartan neighbors + 8D coordinates. Open the MATH section for Weyl orbit, Petrie 30-cycle, and Lie brackets. Press 1–6 to switch views. Press Esc to dismiss this card.