Concept 7 of 8Foundation
Watch on YouTubeVideoTessellations — 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.
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- Q1.Which regular shape tessellates?
- Q2.Three hexagons at a vertex sum to:
- Q3.Why can't a regular pentagon tessellate?
- Q4.Honeycomb is a natural tessellation of:
- Q5.Regular polygons that tessellate alone (there are 3):