Exam 20: Tilings

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

Can the tile below be used to tile the plane?

In a semiregular tiling, what is the maximum possible number of sides of a regular polygon?

Write the vertex type of this semiregular tiling:

Create a tiling with a nonconvex quadrilateral. Is it regular?

If a tiling has only translations, how could it be classified in wallpaper pattern notation?

Create a tiling with a parallelogram. Is it regular?

Squares and equilateral triangles can form a tiling that has at every vertex:

A semiregular tiling has two squares and three regular p-gons at each vertex. What is p?

Tile the plane with a (tileable) pentagon.

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

A non-convex quadrilateral ABCD tiles the plane. What is a possible configuration of the angles at the vertices? I: two types of vertices: 2 As and 2 Cs; 2 Bs and 2 Ds II: one type of vertex: A, B, C, D

A semiregular tiling has two regular octagons and one regular p-gon at each vertex. What is p?

The exterior angle of a regular decagon (10-gon) has a measure of:

Regular dodecagons (12-gons) and equilateral triangles can form a tiling of the plane that has at every vertex:

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

Semiregular tilings can tile with: I: three different regular polygons. II: three different vertex combinations.

A semiregular tiling has two equilateral triangles and two regular p-gons at each vertex. What is p?

Which of the following polygons can tile the plane? I: nonsquare rhombus II: nonequilateral isosceles triangle

Why are Penrose tilings of interest to chemists?