I am trying to replicate the diagram below with grid lines, lines, areas, and labels (corners, coordinates, lines, and areas).
The blue line can be characterized by a line between the points {0.5,0,0.5} to {0.5,0.5,0} or x=.5. The red line can be characterized by a line between the points {0.5,0.5,0} to {0,0.5,0.5} or y=.5. The black line can be characterized by a line between the points {0.5,0,0.5} to {0,0.5,0.5} or x=.5.
Point "a" is just {1/3,1/3,1/3}.
The orange area is y>=0.5 with x+y+z=1. The grey area overlaps partially with z+0.5y>=0.5 and x+y+z=1.
I identified two possibilities (triangle, TernaryListPlot) but got stuck with each.
Option 1: Triangle
Here the coordinates are off and labeling/grid lines seem intensive work:
Show[Graphics[{Line[{{0, 0}, {1, 0}, {.5, Sqrt[3]/2}, {0, 0}}],RGBColor[0, 1, 0], Line[{{0.5, 0}, {0, 0.5}}]}]]
Option 2: TernaryListPlot
Here the diagram structure is there but everything is based on data points and I can't transition from points to lines and areas.
TernaryListPlot[{{0.15, 0.30, 0.55}, {0.25, 0.70, 0.5}, {0.40,0.50,0.10}, {0.80,0.0,0.20}, {0.55, 0.35, 0.10}, {0.30, 0.45, 0.25}, {0.15, 0.40, 0.45}, {0.80, 0.15, 0.05}, {0.45,0.30,0.25}, {0.25, 0.10, 65}}, FrameLabel -> {"A", "B", "C"}]
Thank you in advance for any hints and help!