In the early 1500's Leonardo da Vinci (or an assistant under his direction) created the "octant map," a mappa mundi which splits the globe into eight sections or petals. Each petal is called a Reuleaux triangle--created by joining three equal-length circular arcs into an equilateral triangle. Each cluster of 4 petals covers one hemisphere of the earth.
In terms of cartographic qualities, this projection is neither conformal or equal area†. More so than most projections (Mercator, Peters, Miller Cylindrical, Hobo, etc.), the shape is visually appealing.
For the Art of Geography logo, one cluster of petals was dropped for simplicity's sake (and for it to work better in tiny applications). Apologies to the southern hemisphere.
Leonardo, perhaps best known for his art, undertook surveys of the Italian districts Maremma, Tuscany and Umbria which resulted in six detailed maps. The octant map was possibly created while Leonardo lived in Rome and worked on projects for the Pope. It is reputed to be one of the first maps to label the new world "America."
A possible graticule for the octant map. Leonardo did not include a graticule.
† a conformal projection has the properties that the scale at any point is the same in all directions; and the angle between any two lines on the earth must be the same as on the map. An equal area projection preserves areal relationships; for instance, the Mercator projection is famously not equal area as it distorts the area of Greenland relative to South America.