Entrelac Star

This would be nice as a decoration made of cotton and starched. The example is knit of worsted-weight acrylic. I don't really recommend acrylic for this. The tips of the star tend to twist, and it's easier to block cotton or wool.

Preliminaries

Materials and tools: a small quantity of yarn, with circular knitting needle and crochet hook to suit. A length of smooth, contrasting-color yarn. For the example, 8 inches (20 cm.) is about right.

Right Twist (RT): Knit 2 together, leaving stitches on left needle, then knit the first stitch again and drop the two stitches off the left needle.

You will be knitting five units. The second unit is picked up from the left edge of the first unit, the third from the fourth, and the fourth from the third. The fifth unit is picked up from the left edge of the fourth unit and its own left edge is joined to the cast-on edge of the first unit. The star is finished with a crochet border.

Ignore the brackets if you are knitting a star the same size as the example. The algebra contained within brackets is only useful if you want to make a smaller or larger star. The base number can be any odd number n >= 7. The example uses 11 for n.Cast on 12 [n+1] stitches.

Unit 1

Row 1: (Right side) *YO, RT, K2 [(n-7)/2], K2tog, rep from *.
Row 2: Lay a contrasting piece of yarn from back to front over working yarn, purl to end of row.
Rows 3, 5, ..., 21 [2n-1]: Repeat row 1.
Rows 4, 6, ..., 20 [2n-2]: Repeat row 2.

Leave the last row (21 [2n-1]) on the right needle.

Sanity check: there are 11 [n] lace eyelet holes going up the center of the unit. There are 10 [n-1] loops being held by the contrasting-color yarn.

Units 2-4

Pick up loops held by contrasting yarn onto left needle, from the previous unit's left edge, starting from the bottom left to the top left corner. Remove the contrasting yarn, and use it while turning the rows for this unit.

Row 1: (Right side) *YO, RT, K3 [(n-7)/2 + 1], rep from *.
Rows 2-21 [2n-1]: as for Unit 1.

Leave the last row (21 [2n-1]) on the right needle.

Unit 5

Unpick the cast-on and place the freed-up stitches on the left needle, so that the right side of the first unit is facing you (you start picking up loops from the lower-right corner of the unit toward the lower-left corner). There should be 11 [n] stitches on the left needle. Then with the left needle pick up stitches held by the contrasting yarn. There should now be 21 [2n-1] loops on the left needle.
 
Row 1: YO, RT, K3 [(n-7)/2 +1], YO, RT, K2, SSK, turn.
Row 2: Purl.
Row 3: YO, RT, K2 [(n-7)/2], K2tog, YO, RT, K2 [(n-7)/2], Sl2, K1, PSSO (central double-decrease).
Rows 4, 6, ... 20 [2n-2]: Repeat row 2.
Rows 5, 7... 21 [2n-1]: Repeat row 3.

Leave the last row (21 [2n-1]) on the right needle.

Finishing

Crochet *chain 1, single-crochet in a stitch or yarn-over loop, repeat from * in each stitch or loop around the star. When you get to the inner corners, gather three stitches/loops together into one sc. Finish with a slip stitch into the first single crochet. Block flat.

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