Manuscript VII-F@1 · VII-F.tex · section · 2d81c03f

The active particle link

Cellulation and the isolated particle event › The active particle link · lines 833–853

For $s < 0$ , the link at $P_{s}$ has the cyclic order

e_{0}, V_{0}, e_{1}, V_{1}, e_{2}, V_{2} .

For $s > 0$ , its cyclic order is

u_{0}, U_{0}^{-}, v_{0}^{edge}, U_{0}^{+}, u_{1}, U_{1}^{-}, v_{1}^{edge}, U_{1}^{+}, u_{2}, U_{2}^{-}, v_{2}^{edge}, U_{2}^{+} .

The old edges $e_{i}$ and faces $V_{i}$ are no longer incident to the particle after the event.

The new bisector edges are genuine creases: their adjacent gradients are $(3/5, 0)$ and $(0, 3/5)$ . The ray edges are also genuine creases; after unfolding across a ray, the transverse gradient changes sign. Thus the sixfold star is not produced by merely subdividing a single flat face.

Displayed formulas in this passage

unlabeled · line 836
$e_{0}, V_{0}, e_{1}, V_{1}, e_{2}, V_{2} .$
unlabeled · line 840
$u_{0}, U_{0}^{-}, v_{0}^{edge}, U_{0}^{+}, u_{1}, U_{1}^{-}, v_{1}^{edge}, U_{1}^{+}, u_{2}, U_{2}^{-}, v_{2}^{edge}, U_{2}^{+} .$

The active particle link

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