Exam 20: Tilings

Choose one of Marjorie Rice's pentagon tiles, and use it to tile the plane.

Can the tile below be used to tile the plane?

Can you "tile" space with any regular polyhedron other than a cube?

The interior angle of a regular hexagon has a measure of:

What is a possible way to tile the plane with a hexagon that has four angles measuring 140° and two angles measuring 80°?

Which of the following form the faces of a regular polyhedron? I: six equilateral triangles II: eight equilateral triangles

In the tilings below, which has a fundamental region shown with a heavy outline?

Explain why the tiling below does not form a semiregular tiling of the plane.

Create an Escher-like tiling that uses only translations.

Tile the plane with a (tileable) hexagon.

If you attempt to tile a non-Euclidean surface with five squares meeting at each vertex:

Which of the following regular polygon cannot make a regular tiling?

Use the figure below to tile the plane, if possible.

Use the following information to solve the Questions: Inflation of a sequence of As and Bs consists of replacing each A by AB and each B by A. -If you apply four inflations to B, how many As will you get?

Create a tiling of the plane using squares and hexagons, if possible.

A regular polyhedron with 12 faces has what regular polygon as faces?

A regular polyhedron with 20 faces has what regular polygon as faces?

A scalene triangle ABC tiles the plane. What is a possible configuration of the angles at the vertices? I: three types of vertices: 6 As, or 6 Bs, or 6 Cs II: one type of vertex: 2 As, 2 Bs, and 2 Cs

What is a regular tiling?

What is a possible way to tile the plane with a pentagon with two 90° angles and three equal obtuse angles? I: three at a vertex II: three or four at a vertex