# Course:Harris, Fall 08: Diary Week 12

Mon:

• We confirmed one week from today as the date for Exam 2.
• I explained my (current) scheme for grading the Art Project (artistic porition)
• Artistic Vision
• 10 max (average: 10): adherence to basic requirements
• recognizable figures
• no background between figures
• no overlapping of one figure by another
• 10 max (average: 5): inherent interest or complexity of the pattern
• 3 max (average: 0): bonus for cleverness of motif or theme
• Artistic Execution
• 3 max (average: 2): appropriateness of choice of medium
• 6 max (average: 3): technique of application of medium
• 5 max (average: 4): accuracy of repetition of figures
• 6 max (average: 3): details of outlines of figures
• 6 max (average: 3): detailing interior of figures
• 3 max (average: 0): bonus for overall impressiveness
• Thus, the average project (say, mid-B) will get about 30 points; the maximum possible is 52 (that would be for Escher himself).
• We finished up spherical tessellations:
• We know we can have any number of biangles in a regular tessellation.
• For more "normal" polygons, we found these as the only possibles:
• 4 triangles, 3 at a vertex
• 8 triangles, 4 at a vertex
• 20 triangles, 5 at a vertex
• 6 squares, 3 at a vertex
• 12 pentagons, 3 at vertex
• But are those actually realizable on the sphere?
• We used KaleidoTile to find that, yes, they are each actually spherical tessellations.
• We also used KaleidoTile to look at the corresponding Euclidean solid tessellations:
• tetrahedron
• octahedron
• icosahedron
• cube
• dodecahedron
• We spent the last 15 minutes with groups doing the Hyperbolic Geometry Exploration.

Wed:

• Exam II preparation:
• Practicing drawing a tessellation with a non-convex quadrilateral is a good idea.
• For showing why there are only so many regular tessellations (for plane or sphere), the key is to first look at polygons fitting around a vertex.
• We took about 40 minutes to do Hyperbolic Exploration in Non-Euclid.
• I amended the Exercise assignment (Hyperbolic II) to leave out dual tessellations and finding areas of the basic polygons in Circle I and II.