Candidate sphere structures for the UNLV museum. Each polyhedron is rendered full-width (capped at min(100vh, 100vw) per the brief) and auto-rotates so all sides are visible. Pentagons in the Goldberg variants are accented so the 12-pentagon constraint is legible.
frequency-1 geodesic — 20 triangles
12 vertices · 20 faces · 20× 3-gon
frequency-2 geodesic — 80 triangles
42 vertices · 80 faces · 80× 3-gon
Goldberg GP(1,0) — 12 pentagons
20 vertices · 12 faces · 12× 5-gon
42 faces — 12 pentagons + 30 hexagons
80 vertices · 42 faces · 12× 5-gon · 30× 6-gon
92 faces — 12 pentagons + 80 hexagons (recommended for museum)
180 vertices · 92 faces · 12× 5-gon · 80× 6-gon