Worked Example 1
Show that a regular pentagon does not tessellate.
Step 1: find the interior angleEach interior angle is 540 ÷ 5 = 108 degrees.
Step 2: test it against 360360 ÷ 108 = 3.33..., not a whole number.
Step 3: say what that meansThree give 324, leaving a 36 degree gap. Four would give 432, an overlap. No arrangement closes exactly.
Worked Example 2
Show that a regular hexagon does tessellate, and say how many meet at a point.
Interior angleEach interior angle is 720 ÷ 6 = 120 degrees.
Test360 ÷ 120 = 3 exactly, so three hexagons meet at every point.
Check it against a honeycombCount the cells meeting at a junction in a honeycomb. Always three, exactly as the arithmetic predicts.
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