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Need lacing advice...

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The rim and the spokes are new and from Worksman. The spokes are 10 9/16" - and they match the length on a factory-laced older 26" rim I have. And the older rim is a cross 3. So something's off somewhere. I'll give it another go in the morning. Start in a different hole? Look into a cross 4? Maybe I messed up in what hole I started my third set of 9 in? I really appreciate everyone taking the time with me, here. I'll report back.

Yeah like everyone else is saying, your old wheel is a 4 cross. 10 9/16" should work if you lace them 4 cross. Unfortunately, I don't know of any way to easily correct this, you'll probably need to take it all apart and start over.
 
Another way to determine spoke length and number of cross overs, is to count the even number of spokes between the two most parallel on opposing sides of the flange; the black wheel has 6, while the silver has 8. It is always an even number, so it’s easy to tell if one was missed. (The two most parallel spokes are two spokes apart at the rim; and do not cross each other). One of the near-parallel spokes crosses half of that number; i.e., 3X or 4X.

In the case of the black wheel shown, to convert from 3X to 4X, one may re-do only half of the 36 spokes, 9 on each flange, (the ones laced from the inside of the hub to the outside). When half the spoke nipples are removed, rotate the hub to take up the slack on the remaining spokes, (either all leading or lagging), and resume lacing with the 19th and 28th spokes to be nearly parallel to the spoke which is 180 degrees out at the hub. The 8 other spokes on each side should follow in the correct positions.

The spoke near the “09/“ date stamp would be moved 4 holes over to the hole next to the valve stem.
 
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An update and a word of thanks...
Fact is, I've been a member of quite a few forums for various things. None, as competent, gentlemanly and responsive as this one. I very much appreciate being able to mingle with folks like all of you. Thanks!
In terms of my godforsaken wheel. It's spoked. Pretty much. Truing might be a different story. The runout is a good 3/8" of an inch. I wound up doing a 3 cross - couldn't make a 4 cross work. I spent most of the day fooling with it - took it apart at least a dozen times. I tried copying the assembled (not by me) wheels including following the advice here, and youtube videos. During my fumbling through it, I discovered that my 24" rears (which I'm using the hubs from) are 4 cross. The 26" front is a 3 cross. All that did, was confuse me a bit more, if that's possible. I've never had a project that was so simple, yet so complicated. Spoking is easy, logical stuff...yes?
 
Another way to determine spoke length and number of cross overs, is to count the even number of spokes between the two most parallel on opposing sides of the flange; the black wheel has 6, while the silver has 8. It is always an even number, so it’s easy to tell if one was missed. (The two most parallel spokes are two spokes apart at the rim; and do not cross each other). One of the near-parallel spokes crosses half of that number; i.e., 3X or 4X.

In the case of the black wheel shown, to convert from 3X to 4X, one may re-do only half of the 36 spokes, 9 on each flange, (the ones laced from the inside of the hub to the outside). When half the spoke nipples are removed, rotate the hub to take up the slack on the remaining spokes, (either all leading or lagging), and resume lacing with the 19th and 28th spokes to be nearly parallel to the spoke which is 180 degrees out at the hub. The 8 other spokes on each side should follow in the correct positions.

The spoke near the “09/“ date stamp would be moved 4 holes over to the hole next to the valve stem.
Archie - your advice did the trick...and was much simpler, clearer than any I found. Thank you so much! As an aside - whilst talking to Workman about my order, I asked for advice on 3 Cross/4 Cross lacing. A guy who seemed to know what he was talking about, said something like"...we've done it both ways, depending on how accurate the dimensions on the spokes/rims we got in. So it could be 3 Cross or 4 Cross, depending. To the extent, that you could find both, on the trike we're talking about." Not really comforting, seeing as how I'm working with new rims and spokes ordered from them - the "problem" unfortunately just gets passed along. I have two more wheels to do - and they'll be a breeze, thanks to you.
 
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