Exam 20: Tilings

What is the vertex type?

_____ hexagons can form a tiling of the plane.

What is the maximum number of sides of a regular polygon in a semiregular tiling?

Which of the following polygons can tile the plane? I: regular pentagon II: regular hexagon

A semiregular tiling has an equilateral triangle, a regular hexagon and two regular p-gons at each vertex. What is p?

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

Which of the following polygons can tile the plane? I: scalene triangle II: equilateral triangle

What criterion asserts that a tile can tile the plane by translation plus half-turns under suitable assumptions?

Escher No. 128 [Bird], Figure 20.10 in the textbook, tiles by:

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

What is a possible way to tile the plane with a parallelogram with 60° and 120° angles? I: four at a vertex II: three or six at a vertex

Regular octagons and squares can form a tiling of the plane that has at every vertex:

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

Which of the following is NOT correct for a semiregular tiling?

Tile the plane with a nonsquare rhombus.

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

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. -The inflation of the sequence BBA produces what sequence?

Regular hexagons and equilateral triangles can form a tiling of the plane that has at every vertex:

Illustrate a tiling with the L-tetromino that uses both reflection and rotation.

Why are regular octagons not useable to tile the plane?