Wenninger’s non-convex uniform duals — finite and unbounded displays

All 53 duals of W67–W119: 43 finite and 10 open cut-off displays.
The finite set added 41 complete-face representations.
The medial and great rhombic triacontahedra retain their earlier IDs.
Nine finite snub duals are included, seven with two mirror forms.

Names and uniform construction data: Antiprism, Roger Kaufman / Adrian Rossiter.
Pinned revision 7805b34d3f8860857fb9ac10a1917d1bf4c7888d.
The original source and full MIT notice are retained in data/antiprism/
and the deployed uniform-data-notice.txt.

Primary references:
https://www.antiprism.com/examples/150_named_models/530_uniform_duals/index.html
https://dmccooey.com/polyhedra/
Magnus J. Wenninger, Dual Models, chapter IV (Cambridge, 1983):
https://doi.org/10.1017/CBO9780511569371.007

DW69 denotes the dual of Wenninger W69, not a separate Wenninger book number.
UD13 / DU13 denote the dual of uniform U13. All 75 standard U1–U75 duals resolve
through these aliases, including existing convex and Kepler–Poinsot models.

For a complete original face plane n·x=d, the reciprocal vertex is n/d.
Original edge/face incidence cycles around each uniform vertex order the
dual polygon. This preserves crossed or multiply wound faces, rather than
replacing them with a convex hull. Full faces are rendered by nonzero winding
and perspective-correct depth. Mathematical counts retain original edges
and vertices; crossings add neither. All faces of each finite dual are congruent.

W67, W68, W78, W89, W91, W100, W102, W106, W107 and W119 have central faces.
Their corresponding reciprocal vertices lie at infinity. These ten now use
Wenninger’s symmetric prism-arm convention, cut off openly in both directions.
Primary discussion and illustrations by Guy Inchbald:
https://www.steelpillow.com/polyhedra/StelFacet/infinite/infinite-stars.html

Each central face normal d supplies an ideal direction. At each corner p,
two adjacent noncentral face poles A and B bound an exact parallel strip in
p·x=1. Cuts at d·x=±L retain planar faces and parallel sides; there are no
artificial caps or distant finite substitutes for the ideal vertices.
The adjustable L is 1.25–5 times the farthest finite pole radius (default 2).
The view fits the chosen length. Dashed edges mark the open display cuts.
Finite-vertex dots exclude all artificial cut corners.

F/E/V retain the parent-dual incidence, with V shown as finite + ideal.
Opposite ends are two images of the same ideal vertex; cut edges/corners
are excluded. Coincident elements retain separate incidence identities:
W119’s dual has 60 ideal vertices occupying 30 distinct directions.
V−E+F is a count expression, not a claim about the cut model’s topology.
Prism-arm surfaces can overlap despite differing parent incidence.
Native Antiprism UD resources independently verify all ten finite pole and
ideal-direction spectra. Their distant-point drawing polygons are not used.
Independent three-plane cross-sections and ray checks verify the exact strip
planes, parallel arms, open rims and face picking at cutoff extremes.
Skilling’s exceptional figure has no extra finite reciprocal here.

The small triambic icosahedron is also shown as the exterior boundary mesh S2.
The catalogue distinguishes its twenty complete hexagonal faces from S2’s
sixty exterior pieces, while retaining their separate existing counting
conventions. Other complete-face reciprocals are not silently identified
with exterior stellation meshes.

Independent verification: native Antiprism UD exports for all 43 finite
models; published McCooey edge classes and vertex-radius ratios for 17,
including all 9 finite snub duals; exact incidence/polarity and reciprocal
twice checks; ray-based depth/picking checks for whole and isolated faces.
Original vertex proportions are retained, including very long thin spikes.