The Granthahedron with 16 total sides (8 regular pentagons, 8 irregular pentagons; 8,640° sum of Angles), this version has 1:1.618 (GOLDEN RATIO) irregular pentagons (3 sides = 1 unit sides; 2 sides = 1.618 units sides) appears as an octagonal form when viewed from the top and the bottom.
This is important as the Octagon embodies the SILVER RATIO, defined as 1+(2^.5). When the regular pentagons have sides = 1 unit, the mean length of each side of the Octagon is equal to 1/((1-.618)*2)….when we multiply this value by the SILVER RATIO, the result is that the length across the Octagon is 10^.5 (the square root of 10). (Irregular Triangle inner angles: approx 122.47°; 108.42°; and 78.2°) In Alchemy, this merger of Gold and Silver is the subject of the Alchemical Marriage, the merger of opposites; perfection in the balance of opposites achieved.
The symbol for this union in metallurgy is the Sun and the Moon 🌙 🌞 (with Moon to the left)–notice that this is the same symbol as the Taurus ♉️ (swipe to last photo–just rotated and oriented thus, completing all four orientations of the Bull: α; ♉️; Ω; and now Silvered Gold: PLATINUM and a NEW PLATINUM RATIO to go with it?….1.492
The ratio is derived as follows: {1+(2^.5)} / ({1+(5^.5)} / 2) = 1.492066037647537….).
