OpenOlympiad
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Tessellations — tiling a plane with shapes

A tessellation is a pattern of shapes that covers a flat surface with no gaps and no overlaps. Kitchen floors, beehives, brick walls — all tessellations.

Regular polygons that tessellate alone:

  • Equilateral triangle — 6 meet at a point (6 × 60° = 360°)
  • Square — 4 meet at a point (4 × 90° = 360°)
  • Regular hexagon — 3 meet at a point (3 × 120° = 360°)

Any regular polygon that tessellates must have interior angles that divide 360° exactly. Pentagons (108°) and heptagons don't.

Tessellations often exhibit BOTH reflection and rotational symmetry — beautiful AND mathematical.

Example
Honeycomb cells are hexagonal — perfect tessellation using the least wax per unit space. Bees figured it out a million years before us.
💡 Tip:Designer M. C. Escher made famous drawings of tessellations using lizards, fish, birds — worth looking up.
Prefer a video? Open YouTube search for “tessellation patterns class 6

🎯 Try it!

5 questions to check what you just read.

0 / 5
  1. Q1.Which regular shape tessellates?
  2. Q2.Three hexagons at a vertex sum to:
  3. Q3.Why can't a regular pentagon tessellate?
  4. Q4.Honeycomb is a natural tessellation of:
  5. Q5.Regular polygons that tessellate alone (there are 3):