How to Create a Tri-Hexaflexagon
6-Faced Kaleidoscopic Endless Folding Origami Hexagon
What You Need Before Starting
Folding Instructions (5 Steps)
Follow each step in order. Press your folds firmly against the table using your thumbnail or a ruler for maximum performance.
Score 10 Equilateral Triangles on Paper Strip
Take a strip of paper 2 inches wide by 12 inches long. Measure and score a continuous zigzag pattern of 10 identical equilateral (60-degree) triangles along the strip.
Color or Number the Triangle Faces
On the front side, label the triangles in sequence: 1, 2, 3, 1, 2, 3, 1, 2, 3. Flip over and label the back: 4, 4, 5, 5, 6, 6, 4, 4, 5, 5.
Spiral Wind the Strip into a Hexagon
Count 3 triangles and fold the strip back on itself. Count another 3 triangles and fold underneath. The strip will naturally coil into a neat 6-sided hexagon shape.
Glue the Final End Tab
Tuck the end tab over the front triangle and secure it firmly with a dab of glue stick or clear tape.
Pinch and Flex to Reveal Hidden Worlds!
Pinch three adjacent triangle vertices together toward the center while pushing the opposite valley folds outward. The center will open up like a flower to reveal a brand new face!
Topology & Möbius Surface Mathematics
Discovered by Princeton mathematician Arthur Stone in 1939, flexagons are geometric polygons folded from flat strips that feature hidden topological states. Pinching the adjacent triangles inward inverts the inner vertices, rotating hidden structural layers to the surface like a multi-dimensional Möbius loop.
A tri-hexaflexagon contains exactly 3 distinct faces hidden across 18 interconnected equilateral triangles.
Skills Your Child Develops with This Craft
Mathematical Topology Appreciation
Discovering higher-dimensional folding puzzles expands mathematical wonder and geometric pattern logic.
60-Degree Equilateral Angle Scoring
Scoring exact triangular grid lines sharpens ruler alignment and angle precision.
Pinch-and-Flex Fine Motor Coordination
Executing the triangular three-point pinch grip develops agile thumb and finger coordination.
Fun Family Mini-Games to Play
The Secret Message Decoder Game
Write a secret 3-part riddle across the 3 hidden faces. Challenge a friend or sibling to flex the puzzle to solve all 3 clues.
The Hexa-Hexaflexagon Challenge
Ready for master level? Build an advanced Hexa-hexaflexagon containing 6 different hidden faces made from a 19-triangle strip!
Parent Note:
Flexagons have fascinated mathematicians, physicists, and puzzle-lovers for nearly a century. They make abstract geometry feel playful and tangible.
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