Tile

pentagons refuse. the universe says no.

fit paper tiles round a pin: triangles, squares and hexagons close it; pentagons leave a 36° gap

A corner of a floor is 360°. A regular tile with n sides has a corner of (n−2)×180/n: 60° for a triangle, 90° for a square, 108° for a pentagon, 120° for a hexagon. Only 60, 90 and 120 go into 360 a whole number of times, so only those three tile a floor on their own. Three pentagons make 324°, and the 36° left is smaller than any tile.

Concepts: symmetry, geometry.

An interactive you play with one thumb, on Wundr.