The increase/decrease structure is usually easy to see in eyelet patterns, making them a good place to begin your lace exploration.
Try this ridged ribbon eyelet:
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Cast on an odd number of sts.
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Follow this stitch pattern:
Rows 1 and 3 (RS): Knit.
Row 2: Purl.
Rows 4 and 6: Knit.
Row 5: * K2tog, yo; rep from * to last st, k1.
A pretty way to dress up the ridged ribbon eyelet is to weave narrow satin ribbon in and out of a row of holes. Use a needle and thread to secure the ends. This is particularly effective on baby clothes.
You can also work this cloverleaf eyelet:-
Cast on a multiple of 8 sts, plus 7 sts.
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Follow this stitch pattern:
Row 1 (RS): Knit.
Row 2 and all WS rows: Purl.
Row 3: K2, yo, sl 1, k2tog, psso, yo, * k5, yo, sl 1, k2tog, psso, yo; rep from * to last 2 sts, k2.
Row 5: K3, yo, ssk, * k6, yo, ssk; rep from * to last 2 sts, k2.
Row 7: K1, * k5, yo, sl 1, k2tog, psso, yo; rep from * to last 6 sts, k6.
Row 9: K7, * yo, ssk, k6; rep from * to end of row.
Row 10: Purl.
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Repeat Rows 3–10.