Reuleaux rover rollers

Reuleaux polygons are nifty round-faceted shapes which, remarkably, have constant widths just like the circle. The Reuleaux triangle is the simplest such shape, and has the least area per width; folks may be familiar with it via the 'Wankel' engine and rotary drill bits which make nearly square holes (other familiar Reuleaux shapes are those of the British 20p and 50p coins, which despite their distinctive faceting can be used in vending machines which check the width of a coin rolling through.).

Anyway, spacecraft folks often harp on payload weight as a key factor in mission costs, and look for all kinds of ways to make their precious cargo lighter. As NASA's Mars Rover website says, "Mobility engineers were tasked with making the wheels lightweight, so as not to add any more weight to an already hefty spacecraft; compact, so that when the rover is stowed in the lander they would fit; and capable, so the twin geologists can maneuver off of the lander safely and climb rocks up to ten inches high."

Might all these factors be better served by Reuleaux triangle- shaped wheels than by standard circular ones, especially in rovers with tread-coupled wheels? The Reuleaux rollers would maintain the same constant clearance as circular wheels of the same width; assuming wheels of uniform density, the Reuleaux would weigh 2(pi - 3^.5)/pi -- less than 90% -- as much as the circles; and they would also be that much more compact, the better to fit in NASA's cramped overhead bins.

Of course the Reuleaux rollers would require kinda tricky ellipsoidally floating axles to roll smoothly, which might add back a little of the saved weight, but they still seem worth a look (who says you can't reinvent the wheel?...).