The spherical triangle in this form is known as the Reuleaux triangle, after Franz Reuleaux, who realized that it would roll with a constant diameter.
Moreover, some of the approaches on these pages involve explicit visualization of the spherical octant as a Reuleaux-like spherical triangle, which may well have been what suggested the Reuleaux triangle approach to Da Vinci for his world map.
Details of pages from Leonardo da Vinci's notebook developing the geometry of his octant triangle figure, which was later developed as the Reuleaux triangle [xiii] (Leonardo da Vinci, Paris Manuscript A, 15v; Codex Atlanticus, 923
Also referred to as Al Bahr Towers, the ADIC towers have a unique shape, with their exterior design being based on a Reuleaux triangle
with rounded corners to maximise floor area.