The triangle is favoured because it offers a greater possible richness of association than other base-figures, such as square, hexagon, octagon, or decagon.
The 10 cell face to face path above maps to a 10 vertices path solely traversing along edges in the 600-cell, forming a decagon.
Generally these dishes have ten equal walls (decagon) with a large bowl on one side and a smaller bowl ground out on the other.
The valleys are 10 edge long closed paths and correspond to other instances of the 10-vertex decagon path mentioned above.
On top of the decagon sat an oval dome with a lantern, supported from within by six arches.
The ratio of the side length of the hexagon to the decagon is the golden ratio, so this triangle forms half of a golden rectangle.
In either case, it is best to show the pentagram boundary line to distinguish it from a concave decagon.
A regular decagon has all sides of equal length and each internal angle equal to 144.
