I was looking around in the Unicode block for miscellaneous symbols, U+2600, after I needed to look something up, and noticed there are four astrological symbols for angles: ⚹, ⚺, ⚻, and ⚼.
These symbols are mysterious at first glance but all make sense in hindsight as I’ll explain below.
Sextile
The first symbol, ⚹, U+26B9, is self-explanatory. It is made of six 60° angles and is called a sextile after the Latin word for six.
Semisextile
The second symbol, ⚺, U+26BA, is less obvious, though the name is obvious: semisextile is the top half of a sextile, so it represents an angle half as wide.
The symbol looks like ⊻, U+22BB, the logic symbol for XOR (exclusive or), but is unrelated.
Quincunx
The third symbol, ⚻, U+26BB, represents an angle of 150°, the supplementary angle of 30°. Turning the symbol for 30° upside down represents taking the supplementary angle.
The symbol looks like ⊼, U+22BC, the logic symbol for NAND (not and), but is unrelated.
I’ve run into the name quincunx before but not the symbol. Last fall I wrote a post about conformal mapping that mentions the “Peirce quincuncial projection” created by Charles Sanders Peirce using conformal mapping.
Because the projection was created using conformal mapping, the projection is angle-preserving.
The name of the projection comes from another use of the term quincunx, meaning the pattern of dots on the 5 side of a die.
Sesquiquadrate
The final symbol, ⚼, U+26BC, represents an angle of 135°. A little thought reveals the reason for the symbol and its name. The symbol is a square and half a square, representing a right angle plus half a right angle. The Latin prefix sesqui- means one and a half. For example, a sesquicentennial is a 150th anniversary.
Off-topic, but the term “quincunx” makes me think of a wonderful late-‘80s novel, “The Quincunx”, by Charles Palliser, which is simultaneously a masterful recreation of a 19th century Dickens novel, and a subtle deconstruction of same. A great read…