Hexaflexagon

Hexaflexagon Knitting Pattern by Max Alexander

What Is Being Made

This downloadable PDF contains two knitting patterns for hexaflexagons—geometric toys inspired by the mathematical paper hexaflexagons discovered in 1939 by mathematician Arthur H. Stone and popularized by recreational mathematician Martin Gardner. The first pattern creates a small tri-hexa-flexagon, a flat 3-faced flexing object with 6 unique appearances. The second pattern is a larger trihexaflexagon designed to be worn as a cowl, combining mathematical intrigue with wearable fashion.

Techniques and Construction Methods

These patterns employ traditional knitting techniques adapted to create geometric, three-dimensional structures. The tri-hexa-flexagon construction involves strategic increases and decreases to form the characteristic hexagonal shape that flexes and reveals different colored faces. The flexing mechanism relies on careful stitch placement and shaping to allow the knitted fabric to fold and rotate in the manner of its paper counterpart. The larger cowl version scales up this same geometric principle while maintaining wearability and the interactive flexing quality that makes hexaflexagons engaging toys.

Stitches Used

• Knit (K) - The fundamental stitch forming the base fabric
• Purl (P) - Used in combination with knit stitches for texture and shaping
• Knit 2 together (K2tog) - A right-leaning decrease used to shape the hexagonal form
• Pass slipped stitch over (PSSO) - A left-leaning decrease creating the geometric decreases necessary for the flexagon structure
• Cast on (CO) - The foundation technique for beginning the piece

Materials Required

The pattern specifies DK weight yarn in multiple colors for visual interest and to highlight the different faces of the hexaflexagon. Recommended yarn is Bergere De France Barisienne, a 100% acrylic yarn available in 50g skeins with 140 meters per skein. Color options include Geranium (Red), Igloo (White), Tournesol (Yellow), Methylene (Blue), and Reglisse (Black), allowing crafters to create striking color combinations that enhance the flexagon's geometric appeal. Knitting needles in 3.5mm size are required to work with the DK weight yarn and achieve the proper gauge for the finished pieces.

Difficulty Level

This pattern is rated as intermediate difficulty, making it suitable for knitters with foundational skills who are ready to tackle geometric shaping and multi-color construction. The combination of increases, decreases, and color changes requires attention to detail and understanding of how shaping affects the final three-dimensional form.