Pythagorean Tiling or Tesselation Theory

Regular polygons that can tessellate a plane by themselves

Which of the following is true about regular polygons that can tessellate a plane by themselves?

A) Only polygons with an odd number of sides can tessellate a plane. D) Regular polygons cannot tessellate a plane. C) Any regular polygon can tessellate a plane if scaled properly. B) Only equilateral triangles, squares, and regular hexagons can tessellate a plane.

Rule: To tessellate a plane

What is the primary condition for polygons to tessellate a plane?

C) The polygon must have at least 8 sides. D) The sides of the polygons must all be of different lengths. A) The sum of the interior angles of the polygon must equal 180∘. B) The sum of the interior angles meeting at a vertex must equal 360∘.

Can form a semi-regular tessellation

Which of the following combinations of polygons can form a semi-regular tessellation?

A) Squares and pentagons. C) Equilateral triangles and heptagons. D) Octagons and hexagons. B) Hexagons and equilateral triangles.

Regular polygon that can tessellate

How can you determine if a regular polygon can tessellate a plane by itself?

C) The sum of the interior angles of the polygon must equal 360∘ B) The interior angle divided by 60∘ must be a whole number. A) The interior angle of the polygon must divide 360∘ evenly. D) The polygon must have more than four sides.

Pythagorean Tiling or Tesselation Theory

Regular polygons that can tessellate a plane by themselves

Rule: To tessellate a plane

Can form a semi-regular tessellation

Regular polygon that can tessellate

Information: Pythagorean Tiling or Tesselation Theory