Proposition: Complete transverse noncentral data

The capped transverse patch has eight two-dimensional faces and 25 actual edges on either regular epoch. Its noncentral edge classes are:

Every noncentral edge has length greater than $1/2$. The only transverse incidence change is the central exchange.

Proof. The vertices are the two central endpoints, four inner corners, four inner side midpoints, four outer corners, and four outer side midpoints. The central edge and four mixed arms, followed by the listed collar edges, exhaust their incidences.

For the incoming northeast arm, the displacement is $X_s(p,1,p/q)$ in $(t,x,y)$. Its squared norm is ${X_s}^{2}1921/625$. For the outgoing arm use $Y_s(q,q/p,1)$, with squared norm ${Y_s}^{2}1921/1521$. These give the arm formulas, which agree at zero. All remaining edges are horizontal and have the listed Euclidean lengths.

The smallest collar-join length is $3/5$; the arms exceed $3\sqrt{1921}/25$. All faces have open interiors: core faces near their inner side midpoints and collar faces by the strict margins. The central dominance calculation then isolates the only transverse incidence change.