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Regular hexagons and equilateral triangles

Regular hexagons and equilateral triangles-example-1

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Regular Hexagons and Equilateral Triangles: Yes, a semiregular uniform tessellation can be created with regular hexagons and equilateral triangles.

Here's why:

Internal angle of hexagon: 120 degrees

Internal angle of equilateral triangle: 60 degrees

Since 120 + 60 = 180, three 60-degree angles (from equilateral triangles) can perfectly fill the gap between two 120-degree angles of a hexagon. This arrangement allows for a seamless and repeating pattern, satisfying the criteria for a tessellation.

Number of Shapes Needed at Each Vertex:

At each vertex of a hexagon, 3 equilateral triangles meet.

At each vertex of an equilateral triangle, 2 hexagons meet.

Therefore, a semiregular uniform tessellation can be created with regular hexagons and equilateral triangles, with the arrangement described above.

Complete question:

Determine whether a semiregular uniform tessellation can be created from the given shapes, assuming that all sides are 1 unit long. If so, determine the number of each shape needed at each vertex to create the tessellation.

Regular hexagons and equilateral triangles

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