Just a thought, but why not use multiple strokes on a single path. You can add more stroke in the apprearence panel. Alternate between white and black making each stroke larger as you go. Just make sure the largest stroke is on the bottom and smallest on top, so they are all visible.
I'm not sure how to do that. Can you explain how to do it more? maybe with steps?
Just a quick note, this applies the stroke to both sides of the path. You could either clip the outside by copying the path and pasting it in front. Select both paths and choose Object>Clipping path make. This option would hide the outside portion of the bottom path.
Or on the front path, remove the extra strokes in the appearance panel, so that has only 1 stroke. Then give it a fill that matches the background. This option would cover up the inner portion of the bottom path.
And now for another way.
Create your path and give it a stroke.
Now goto object>path>offset path and type in a spacing of approx. 10 px to start. undo and repeat of not right.
repeat the offset path as many time as you like.
It can get a bit repetitive but it works.
Just a quick note, this applies the stroke to both sides of the path.
Not if choosing Align to Inside or Outside in the Stroke panel which works for closed paths.
As I understand it, you are drawing the white polygons with different thickness but want the same space between them? If so, I would do it like this
1. draw strokes with desired different width and distribute them as shown
2. drag the strokes to the Brushes panel to create an art brush and apply it to a polygon
3. Object > Expand Appearance, select the disconnected half and delete it
4. Use the Reflect tool to make a reflecting copy, with the black pointer select each of the corresponding pairs and join (Ctrl +J)
To add new strokes, in the Appearance palette flyout (top right arrow) tick Add New Stroke, then make sure you have it selected in the main Appearance palette when you change it.
For stroke/nofill hexagonal paths, you can also use Object>Path>Offset Path setting the Offset to equal the sum of the (new) Stroke Weight and the desired gap. For identical Stroke weights and gaps you can just repeat it.
However, it seems that your hexagon shapes are fill/nostroke compound paths forming rings of increasing size, and none of the suggested ways would work with that.
It is much easier to work with stroke/nofill paths, unless you wish to have scaled shapes, with increasing gaps and thicknesses.
You can scale either; for stroke/no fill paths you need to tick Scale Strokes & Effects, which you can do in the Transform palette flyout.
If you wish to have hexagons of different widths but with identical gaps, as keenly spotted by Emil, for a stroke/nofill version you may also:
1) Create the innermost hexagon,
2) Scale a copy to get the outermost hexagon and adjust its Stroke Weight if needed,
3) Object>Blend>Options, set the number of intermediate hexagons,
4) Select both and Object>Blend>Make, you may need to go back and adjust the size of 2),
6) Align>Distribute Spacing.
I think Jacob actually meant Distribute Objects.
Just tried it using Vertical and Horizontal centers but these options don't use the preview bounds leaving the distribution unchanged because the strokes are already distributed perfectly. The task is to make the gaps between each different weight stroke the same. CS5 on Windows
I obviously ran out of sensible things to say after the second suggestion. Sorry.
Wow. these are all great solutions. I will try out all of them to see what works best for me. Thank you guys so much.