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ILS 4430

Exam 2

NAME: ____________________________

The following exam is worth 75 points.

While you are completing this exam, you may refer to any of the following:

•

•

•

•

Materials posted to Ulearn for ILS 4430.

Any textbook, including the ILS 4430 textbooks.

Any website that is purely informational.

You-Tube, Kahn Academy, or similar videos.

You may also discuss problems that are similar to the exam problems with others, including myself.

In reference to completing the specific eight problems on this exam, you may not collaborate with or

obtain help from others in any way. This includes but is not limited to fellow students, friends, family

members, and tutors. Question and answer websites are also prohibited.

If I suspect the work you submit for this exam is not your own, you will need to defend your work in a

Zoom meeting before you receive a grade.

1

(T12) Problem 1: Classify each pattern as either 0° ,60°, 90°, 120°, or 180°, according to the smallest

(6 points)

angle of rotation in the pattern.

(a)

(b)

Angle:

Angle:

(T13) Problem 2: Classify the following frieze patterns in “Hop-Step-Jump” notation.

(12 points)

(a)

(b)

Hop-Step-Jump Notation:

Hop-Step-Jump Notation:

(c)

(d)

Hop-Step-Jump Notation:

Hop-Step-Jump Notation:

2

(T14) Problem 3: Classify each wallpaper pattern as either p111, p1m1, p1g1, or c1m1.

(6 points)

(a)

(b)

Pattern:

Pattern:

(T14) Problem 4: Classify each wallpaper pattern as either p211, p2mm, p2mg, p2gg, or c2mm.

(6 points)

(a)

(b)

Pattern:

Pattern:

(T15) Problem 5: Classify each wallpaper pattern as either p411, p4gm, or p4mm.

(6 points)

(a)

(b)

Pattern:

Pattern:

3

(T15) Problem 6: Classify each wallpaper pattern as either p311, p31m, or p3m1.

(6 points)

(a)

(b)

Pattern:

Pattern:

(T15) Problem 7: Classify each wallpaper pattern as either p611 or p6mm.

(6 points)

(a)

(b)

Pattern:

Pattern:

4

(T16) Problem 8: Cross out any vertex configurations that violate the given rule. You may cross out

more than one vertex configuration for each rule.

(12 points)

Rule 1: In a semiregular tiling of the plane, the sum of the vertex angles of the polygons meeting at each

vertex must be exactly 360°.

(a) 3.3.6.6

(b) 4.8.4

(c) 3.4.9

(d) 7.7.8.12

Rule 3: No semiregular tiling can have four or more different polygons meeting at a vertex. Thus, if a

semiregular tiling has four or more polygons meeting at a vertex, there must be some duplicates.

(a) 3.4.9

(b) 8.9.10.11

(c) 5.6.6.11

(d) 4.7.8.9.11

Rule 4: No semiregular tiling with exactly three polygons meeting at each vertex can have the vertex

configuration k.n.m where k is odd unless n = m.

(a) 5.7.7

(b) 3.7.8.12

(c) 6.9.11

(d) 3.3.8

(T17) Problem 9: Construct the dual tiling of the tiling.

(7 points)

5

(T17) Problem 10: Circle any of the following tiling modifications that have been used in the Escher-type

tiling. You may circle more than one tiling modification.

(8 points)

(a) translation

(b) glide reflection

(c) midpoint rotation

(d) side rotation

6

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math calculations

frieze patterns

Classify each pattern

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