All
I've been building wheels for a few years now, and had a surprising experience this weekend which prompted a question.

I was swapping out the wheels on my commuter, putting on a set that was among the 1st I had ever built. I noticed that on the front wheel (32 spokes built 3-cross with a disc brake) I had not crossed the outbound spokes under the 3rd spoke they crossed! Don't know how I did that, I checked all my other wheels and they were as expected.

The thing is, I've put 2000 miles on that wheel and I go down some pretty steep hills. The wheel was true and round (although I did undo the spokes and cross them as they should be). So my question is, why do we cross the spokes? It's a bit of a pain and sometimes I scratch the rim w/ the spoke I am trying to cross Was my wheel a fancy radial lace or was I just very lucky?

Thanks -

the basket weaving the last cross does a bit for the load sharing.. for side loading of velodrome track wheels

the builders would further wrap that last cross with copper wire and solder it.

radially spoked wheels can pull a chunk of hub flange out..

I'm told radial spoked wheels in front of CX bikes became popular as less grass got stuck in the crosses.

Your build isn't a "fancy radial lace", it's a 3X that isn't interlaced.
Radial means that if you were to extend the spokes inwards, they'd cut through the axle. Interlaced is that over/under thing that has the spokes straining against each other.

All things considered, it's not a big deal, particularly for a front.
Interlacing is supposed to help keep the "pushing" spoke taut,(for a rear) while non-interlaced is supposed to make a wheel feel more responsive on takeoff.

The reason for over/under interlacing at the crosses is that it introduces a certain amount of resiliency into the finished wheel. The spokes don't go straight from hub to rim, but instead have a bit of shallow bend on the way,

When a spoke is stressed, the bend can accommodate the load by being pulled straighter at the expense of the partner spoke, splitting the effect so neither spoke sees as much change in tension as they would if not laced. Since spokes break through metal fatigue induced through cyclic tension changes, this approach increases the long term life expectancy of a wheel.

This benefit works both in the direction of mitigating stress increases and, possibly more significantly, reducing the effects of tension reduction so that a spoke that might otherwise reach zero tension doesn't.