Zigzag structure of prisms over antiprisms

Let $APrism_m$ be the $m$-parameter antiprism, and let $Prism(APrism_m)$ denote the prism over it. Write $z$ for the zigzag vector and $Int$ for intersection vectors. Prism-over-antiprism conjecture. The prism over $APrism_m$ has

$$z=\left(\frac{8m}{\gcd(m,3)}\right)^{8\gcd(m,3)},$$

with $Int=(\frac{2m}{3})^4$ if $\gcd(m,3)=3$; otherwise, two zigzags have $Int=(0,2m)^4$, two have $Int=(0,2m),(2m,4m)$, and four have $Int=(0,2m)^2,(0,4m)$. The formula is part of the paper's broader conjectural description of prism zigzags; the supplied text gives no proof or resolution.