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Tessellations: Shapes That Tile Forever

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.

The two golden rules

For shapes to tessellate, they must follow two rules. Tap each tile pattern below to check it.

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Tap me
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Tap me

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!

Tap every shape that tiles forever

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.)

Square
Triangle
Hexagon
Circle
Pentagon

Tap the shapes that tile with no gaps. Find all 3!

Surprise: a regular pentagon leaves gaps, but squares, triangles and hexagons tile perfectly. 🔺

The corner secret: 360°

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!

Build a tiled wall

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. 🧱

Tessellations are everywhere!

Tap each card to reveal a real-life tessellation you can spot.

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Honeycomb
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Turtle shell
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Brick wall
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Floor tiles

Tap a card… how many can you uncover?

Make your own pattern

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. 🐦🐟

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You did it!

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! ⭐