
<Update 2/15/07> - Metro has officially decided to go square as stations are fixed, updated, or built new. More information here.
<Original Post>
According to the Washington Post (”Board of 2 Minds About 6-Sided Tiles“, 10/20/06), the Washington Metropolitan Transit Authority (WMTA) is considering moving from 4.5 inch sided hexagon tiles (above) to 12 inch sided square tiles of the same color (see report here). The old hexagonal tiles are slippery when wet and have too many joints at subway pick-up spots, inherent character flaws which are causing much consternation among conservatives. Who knew DC had such lavicious floor coverings?
The WMTA Board is asking the currently homo-tilic manufacturer of the proposed square tiles to look into “switching teams” and producing hexagonal tiles to keep the unique subway aesthetics, reportedly because “6-ways are more fun.” A WMTA architect was quoted as saying that square tiles are more closely aligned with conservative ideals because “Fewer sides means fewer joints. Fewer joints means less water leakage damaging concrete below the tiles.” The concrete has thus far remained silent on whether the joints and leakage were in fact “damaging.”
The area of the new square tiles would be 1 ft2 each, while the old hexagonal ones are 0.4 ft2, which is hardly a fair competition. As a result of the handicap, mathmatically the squares would have more AND longer joints. However, if an extreme makeover hexagonal tile also had an area of 1 ft2 (6.9 inches/side), the hexagons come roaring back to reduce the length of the joints, even if they have more joints:
1. Length of joints: The length of the joints, i.e. perimeter, for a fixed surface area is less with a hexagon than a square. A hexagon with a 6.9 inch sides (vs. current 4.5 inches) would have a perimeter of 3.5 ft and an area of 1 ft2 (the same as the new square tiles). The 1 ft sided square tiles, having the same surface area, lose out with a 4 ft perimeter - that’s an extra 0.5 ft per tile!!! Hexagons win! Hexagons win!
2. Number of joints: With the area of both tiles fixed at 1 ft2, the fight is on to cover a hypothetical 10,000 ft2 with 10,000 tiles…the square tiles will have 20,200 joints, while the hexagons would have about 43,000 joints. Squares win by a 2:1 margin!!!
The WMTA could have saved a lot of money by hiring honeybees instead of consultants to figure this out eons ago. Honeycomb uses hexagons to maximize surface area, while minimizing perimeters and avoiding wasted space between the joints - so efficient! And for you wiseguys, a circle with an area of 1 ft2 has a perimeter of just over 3.5 ft2 (similar to the hexagon), but results in a lot of wasted space between them (for grout or honeycomb) when spaced next to one another.
I have no idea whether joint failure is a function of the number or length or a grout-raid but the debate is probably mute anyway - the WMTA is likely jumping into bed with the New York City subway on a square tile purchase deal. Hexagons, your days are numbered…
Props go out to MathTrek for the story lead…