Exam 20: Tilings

Escher No. 6 [Camel], Figure 20.15 in the textbook, tiles by:

A semiregular tiling has one square, one regular hexagon, and one regular p-gon at each vertex. What is p?

Any finite portion of a Penrose tiling can be found in another Penrose tiling.

If 4.8.n is a possible vertex type for a vertex surrounded by regular polygons, what is n?

What are the possible rotational symmetries of a crystal?

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

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

_____ pentagons can form a tiling of the plane.

Create a nonregular tiling with a right triangle tile.

Write the vertex type of this semiregular tiling:

What is a possible way to tile the plane with a general isosceles triangle? I: six at a vertex II: four or eight at a vertex

What is a semiregular tiling?

Tile the plane with an equilateral triangle.

Give a numerical explanation of why a regular decagon (10 sides) cannot tile the plane by itself.

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. -Two inflations of A produce what sequence?

_____ nonconvex quadrilaterals can form a tiling of the plane.

Can the tile below be used to tile the plane?

Which of the following is a regular tiling of the plane?

Can the tile below be used to tile the plane?

Can the tile below be used to tile the plane?