Exam 20: Tilings

Create a nonregular tiling with octagons and squares.

Portions of Penrose tilings can have rotational symmetry.

Create an Escher-like tiling that uses only translations and reflections.

Which of the following is NOT possible for a number of sides of a regular polygon in a semiregular tiling?

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

Escher No. 67 [Horseman], Figure 20.11a in the textbook, tiles by:

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

List all regular tilings.

At the vertex of a tiling of the plane there are two regular pentagons and one regular p-gon at each vertex. What is p?

Can the tile below be used to tile the plane?

Create an Escher-like tiling that uses only translations and half-turns.

At the vertex of a tiling of the plane there is a regular octagon, a square, and one other regular polygon. Which regular polygon is it?

Create a tiling of the plane using triangles and octagons, if possible.

The exterior angle of a regular octagon (8-gon) has a measure of:

A semiregular tiling has four equilateral triangles and one p-gon at each vertex. What is p?

Why are regular pentagons not usable to tile the plane?

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

Can the tile below be used to tile the plane?

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

_____ convex quadrilaterals can form a tiling of the plane.