Tessellations
Math ⇒ Geometry
Tessellations starts at 7 and continues till grade 12.
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Describe a real-world application of tessellations.
Describe the process for determining if a regular polygon can tessellate the plane.
Describe the role of symmetry in tessellations.
Explain the difference between a regular tessellation and a semi-regular tessellation.
Explain the term 'vertex configuration' in the context of tessellations.
Explain why regular pentagons cannot tessellate the plane by themselves.
Given a tessellation pattern where each vertex is surrounded by two squares and three equilateral triangles, what is the vertex configuration?
Given a context: A designer wants to create a tessellation using only regular polygons where each vertex is surrounded by one square, one regular hexagon, and one regular dodecagon. Is this tessellation possible? Justify your answer mathematically.
Which of the following combinations of regular polygons can form a semi-regular tessellation?
(1) Squares and equilateral triangles
(2) Pentagons and hexagons
(3) Hexagons and octagons
(4) Triangles and pentagons
Which of the following is a property of a tessellation?
(1) The pattern leaves gaps
(2) The pattern overlaps
(3) The pattern covers the plane completely
(4) The pattern uses only circles
Which of the following is a semi-regular tessellation?
(1) Only squares
(2) Only hexagons
(3) Squares and octagons
(4) Only triangles
Which of the following is NOT a requirement for a shape to tessellate the plane?
(1) The shape must be regular
(2) The shape must cover the plane without gaps
(3) The shape must cover the plane without overlaps
(4) The shape must be able to repeat infinitely
A tessellation is a pattern of shapes that covers a plane with no _______ and no _______.
A tessellation is also known as a _______ in mathematics.
A tessellation is said to be periodic if it _______.
If a tessellation is made from two or more types of regular polygons, it is called a _______ tessellation.
If a regular polygon has an interior angle of 120°, can it tessellate the plane by itself?
True or False: A regular pentagon can tessellate the plane by itself.
True or False: A tessellation can be made using non-convex polygons.
True or False: All quadrilaterals can tessellate the plane.
