Reconstructing the Banias Floor
Step 1: Begin with the tile that has the greatest number of sides, the octagon.
Step 2: Because only the base of the black triangle matches the length of the octagon’s individual sides, arrange eight black triangles around the multicolor octagon. This creates a 90-degree angle between each pair of black triangles.
Step 3: Since only the smaller multicolor squares fit in that space, arrange those between each pair of black triangles. The result is the basic pattern module: an eight-pointed star, which was a popular motif in the Roman Empire.
Step 4: Repeat that pattern on all four sides of the first module, overlapping some of the squares.
Step 5: Notice a problem? Some of the squares abut other squares of the same color, contrary to the rule that each side of a tile must border with a tile of contrasting color. Remedy: Cut such squares in half along the diagonal, thus creating two isosceles right triangles (triangle with right angle between two sides of equal length); then replace either with a black one. This solution also accounts for the presence of isosceles right triangles in both black and multicolored materials found at Banias.
Step 6: The modified module can be replicated indefinitely, to create a large floor. The resulting effect is worthy of King Herod the Great.