Increasing the Honeycomb Mesh

The Honeycomb Mesh pattern is widely used as a background pattern in knitted lace design. It is versatile, stretchy, and easy to memorize and knit. In my opinion, these virtues have led to this pattern's being both overused and abused in the service of lace design. Because it tolerates being stretched, squeezed, and distorted, it can be made to flow around virtually any foreground pattern, no matter how fanciful.

This hexagonal pattern is the ground of choice for many of the most beautiful lace works available to knitters. The typical way of increasing this pattern is by adding cells around the edges of the foreground pattern, as is done around the central star in this doily. I wanted to explore it for its own merits, starting with finding a way to work increases within the mesh pattern itself.

Here's what I came up with. Honeycomb Mesh is worked on a multiple of 4 stitches, with patterning on alternate rounds, and alternate rounds knitted plain (with k1 p1 into double yo's).

How to Increase

| = k
/ = k2tog  
\ = SSK (or sl 1, k1, psso)
O = yo

This shows an increase at a single column of hexagons. 
How frequently to increase around the whole circle 
depends on your design goal. Six points of increasing, 
with increases every third pattern round, should 
give a hexagon.

\ O O / \ O O / \ O O / \ O O /   9
| | | | | | | | | | | | | | | |   8
O / \ O O | | O O | | O O / \ O   7  increases by 4 sts
| | | |   | |     | |   | | | |   6       at one place                                                                                                                                                                                                                                                      
\ O O /   \ O     O /   \ O O /   5
| | | |   | |     | |   | | | |   4
O / \ O   O /     \ O   O / \ O   3
| | | |   | |     | |   | | | |   2
\ O O /   \ O     O /   \ O O /   1
| | | |   | |     | |   | | | |   0  Start with multiple
                                          of 12 sts

If you want to double the number of stitches, as shown 
in the doily, work round 7 with k1 where decreases are 
shown. That is, yo, *k2, yo twice* around; end k2, yo.