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Triangular antiprisms: Two faces are equilateral, lie on parallel planes, and have a common axis of symmetry. The other six triangles are isosceles. The regular octahedron is a special case in which the six lateral triangles are also equilateral. Tetragonal bipyramids, in which at least one of the equatorial quadrilaterals lies on a plane. The ...
A regular hexagram, , can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram or sexagram is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}.
Hexagram 64 is named 未濟 (wèi jì), "Not Yet Fording". Other variations include "before completion" and "not yet completed". Other variations include "before completion" and "not yet completed". Its inner (lower) trigram is ☵ ( 坎 kǎn) gorge = ( 水 ) water, and its outer (upper) trigram is ☲ ( 離 lí) radiance = ( 火 ) fire.
The two tetrahedra of the compound view of the stellated octahedron are "desmic", meaning that (when interpreted as a line in projective space) each edge of one tetrahedron crosses two opposite edges of the other tetrahedron. One of these two crossings is visible in the stellated octahedron; the other crossing occurs at a point at infinity of ...
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two ...
Next the fourth line of hexagram 6 is changed to produce hexagram 7. Changing the first three lines of hexagram 7 produces hexagram 8. These eight hexagrams are of the same element as the original hexagram that was made by doubling a trigram. For example, the house of the first hexagram is:
There are 64 possible permutations. The 64 hexagrams and their descriptions make up the book. The trigram symbolism can be used to interpret the hexagram figure and text. An example from Hexagram 19 commentary is "The earth above the lake: The image of Approach.
An adapted unicursal hexagram is an important symbol in Thelema. In Aleister Crowley's Thelema, the hexagram is usually depicted with a five-petalled flower in the centre which symbolises the pentagram. The hexagram represents the heavenly macrocosmic or planetary forces and is a symbol equivalent to the Rosicrucian Rose Cross or ancient ...