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Children will easily find that triangles, quadrilaterals, and hexagons can tessellate on their own. The other shapes of the Geometric Cabinet are more challenging. In our last blog, we discussed tessellating nonagons. This time we will address heptagons.

The 7-sided heptagon cannot tessellate on it's own. This is the first discovery. The heptagon will require a partner shape in order to tessellate.

Combining the heptagon with isosceles trapezoids will generate a repeated linear pattern.

But, this pattern cannot tessellate.

Add an obtuse scalene triangle to the mix and this pattern:

can tessellate (shown below)!

Alternately, arranging the heptagons in an elliptical pattern will reveal a double irregular pentagon opening in the center.

Each irregular pentagon can be formed by combining an obtuse angle scalene triangle and an isosceles trapezoid.

This reveals the same tessellating pattern (just looking at it from a different angle)!

See our Heptagon Trapezoid Triangle Tessellation Pattern Blocks for sale in our product catalog.

1/19/2013