The flag of Togo features a design consisting of five horizontal stripes and a red square in the upper hoist-side corner. The aspect ratio of the flag is 1:1.618, known as the golden ratio.

Colors and their corresponding HEX color codes:

1. Green (top and bottom stripes): #008751
2. Yellow (second and fourth stripes): #FFD700
3. Red (square in the top-left corner): #DE3831
4. White (five-pointed star inside the red square): #FFFFFF

Geometric properties:

1. Each of the five horizontal stripes has an equal width.
2. The width of the red square is equal to the width of three horizontal stripes.
3. The white five-pointed star is inscribed within an invisible circle centered on the red square, with a diameter that is 2/5ths of the square's width.

No specific measurements are assigned to the flag, as it can be scaled up or down while maintaining the proportions mentioned above.