One-Color Honeycomb Brioche Stitch
Honeycomb brioche creates a very thick fabric so you should use the normal needle size (unlike plain brioche where you would use a smaller needle). If you knit it in fine yarn on large needles it makes a beautiful lace. Please note that there are 2 preparatory rows. Bind off very loosely on a RS row, knitting together the k1 and yo of last row as one stitch, with a much larger needle.One-Color Honeycomb Brioche – RS                                 One-Color Honeycomb Brioche – WS

Loosely an even number of sts.
Set-Up Row 1 WS: *k1, sl1yo; rep from * .
Set-Up Row 2 RS:  go behind the yo of first st and k this first st (not with its yo), *wyib, slip the yo pwise, k2 (meaning k1, then go behind the foll yo and k1); rep from *, end wyib, slip the yo pwise, k1.
Row 1 WS: *sl1yo, brk1; rep from *.
Row 2 RS: *k2 (as in Set-Up Row: 2), wyib, slip the yo pwise; rep from *.
Row 3 WS: *brk1, sl1yo; rep from *.
Row 4 RS: yarn is hanging over needle to front, take yarn under needle to back so that the yo from former row is maintained, k1 (without the yo), *wyib, slip the yo pwise, k2 (as in row 2); rep from *; end with k1.
Rep from Row 1 WS.

Two-Color Honeycomb Brioche Stitch
Use either circular or double-pointed needles to avoid having to cut threads. This brioche stitch treats the yarnover as a separate stitch.Two-Color Honeycomb Brioche – LS                               Two-Color Honeycomb Brioche – DS

Loosely cast on an even number of sts with dark color DC.
Set-Up Row DS LC: *sl1yo, k1; rep from *. Do not turn, slide.
Set-Up Row DC DC: *slip the yo pwise, p2; rep from *. Turn work.
Row 1 LS LC: *sl1yo, brp1; rep from *. Do not turn, slide.
Row 1 LS DC: *go behind yo and k1, slip yo pwise, k1; rep from *, end with go behind yo and slip it pwise, k1. Turn work.
Row 2 DS LC: *sl1yo, brk1; rep from *. Do not turn, slide.
Row 2 DS DC: *slip the yo pwise, p2; rep from *. Turn work.
Rep Rows 1 and 2, LC and DC.
Repeat from Rows 1 LS LC.

Three-Color Honeycomb Brioche Stitch
Use either circular or double-pointed needles to avoid having to cut threads. This brioche stitch works the yarnover as a separate stitch. The dark color (color A) is always used as the background color, so it is worked every other row. When you attach a new color I would advise you to knot it to another thread to help maintain yarnovers at the end of rows. My colors: color A = dark blue, color B = medium blue, color C = light blue.Three-Color Honeycomb Brioche – RS                              Three-Color Honeycomb Brioche – WS

Loosely cast on an even number of sts using color A. Attach color B
Set-Up Row: WS Color B: *sl1yo, k1; rep from *. Do not turn, slide. Slide to other end of needle to pick up Color A.
Set-Up Row: WS Color A: *wyif, slip the yo pwise, p2; rep from *. Turn work. Attach color C.
Row 1 RS Color C: *sl1yo, brp1; rep from *. Do not turn, slide. Slide to other end of needle to pick up Color A.
Row 2 RS Color A: *go behind yarnover and k1, slip the yo pwise, k1; rep from *, end with go behind yo and slip it pwise, k1. Do not turn, slide. Slide to other end of needle to pick up Color B.
Row 3 RS Color B: brk1, sl1yo; rep from *. Turn work. 
Row 4 WS Color A: *wyif, slip the yo pwise, p2; rep from *. Do not turn, slide. Slide to other end of needle to pick up Color C.
Row 5 WS Color C: maintain yo from prev row so that you can work the first st, *brk1, sl1yo; rep from *. Turn work.
Row 6 RS Color A: *go behind yo and k1, slip the yo pwise, k1; rep from *, end with go behind yo and slip it pwise, k1. Turn work. 
Row 7 WS Color B: *sl1yo, brp1; rep from *. Do not turn, slide. Slide to other end of needle to pick up Color A.
Row 8 WS Color A: *slip the yo pwise, p2; rep from *. Do not turn, slide. Slide to other end of needle to pick up Color C.
Rep from Row 1 RS Color C.