A tessellation is a pattern of shapes that fit together perfectly — no gaps and no overlaps — and could go on forever in every direction.
Bees build honeycombs out of tessellating hexagons! 🐝
Let's discover which shapes tile forever — and play with making patterns yourself. Tap Next to begin.
For shapes to tessellate, they must follow two rules. Tap each tile pattern below to check it.
Tap a pattern to reveal its secret…
Rule 1 — No gaps: no empty spaces left over.
Rule 2 — No overlaps: shapes never sit on top of each other.
Circles fail because round edges leave little gaps. Straight edges fit much better!
Some shapes fit together on their own; others leave gaps. Tap the ones you think tessellate. (Hint: think about whether copies fit edge-to-edge.)
Tap the shapes that tile with no gaps. Find all 3!
Surprise: a regular pentagon leaves gaps, but squares, triangles and hexagons tile perfectly. 🔺
Where corners meet at a point, the angles must add up to exactly 360° — a full turn — with no space left.
Add tiles around the centre dot. Try to reach exactly 360°!
Total: 0°
Six triangles (6 × 60° = 360°) close up perfectly. That's WHY triangles tessellate!
A real tessellation has no empty spaces. Tap the squares to lay tiles and fill the whole wall — every cell must be covered!
0 of 36 tiles laid. Fill them all!
Tiles, bathroom floors and brick walls are everyday tessellations. 🧱
Tap each card to reveal a real-life tessellation you can spot.
Tap a card… how many can you uncover?
Pick a colour, then tap the triangles. The same shape repeats — but YOUR colours make a brand-new design!
Tap triangles to colour them. Colour at least 6!
Artist M.C. Escher made amazing tessellation pictures of birds and fish. 🐦🐟
You now understand shapes that tile forever.
🔑 Tessellation = shapes that fit with no gaps and no overlaps, repeating forever.
🟩 Squares, triangles and hexagons tessellate on their own.
🔴 Circles and regular pentagons leave gaps, so they don't.
🎯 The corner secret: angles meeting at a point must add to 360°.
🐝 Look for tessellations in honeycombs, brick walls, floor tiles and turtle shells!
Well done, tessellation star! ⭐